Max order of an isogeny class of rational elliptic curves is 8?For which composite $N$ does $X_0(N)$ possess a non-cuspidal rational point?About isogeny theorem for elliptic curvesMust the $j$-invariant of an elliptic curve with an isogeny be integral?Elliptic curves over QQ with isomorphic n-torsion$j$-invariants of elliptic curves over finite fieldstwists of elliptic curves over finite fields
Max order of an isogeny class of rational elliptic curves is 8?
For which composite $N$ does $X_0(N)$ possess a non-cuspidal rational point?About isogeny theorem for elliptic curvesMust the $j$-invariant of an elliptic curve with an isogeny be integral?Elliptic curves over QQ with isomorphic n-torsion$j$-invariants of elliptic curves over finite fieldstwists of elliptic curves over finite fields
$begingroup$
I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been settled? And if so, what is a reference to the proof of the result.
nt.number-theory reference-request elliptic-curves
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
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add a comment |
$begingroup$
I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been settled? And if so, what is a reference to the proof of the result.
nt.number-theory reference-request elliptic-curves
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
$endgroup$
add a comment |
$begingroup$
I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been settled? And if so, what is a reference to the proof of the result.
nt.number-theory reference-request elliptic-curves
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
$endgroup$
I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.
Theorem 5 There is a constant $C$ such that every elliptic curve $E_/mathbbQ$ is isogenous (over $mathbbQ$) to at most $C$ (mutually nonisomorphic) elliptic curves.
"Can one take $C=8$?"
Has this question been settled? And if so, what is a reference to the proof of the result.
nt.number-theory reference-request elliptic-curves
nt.number-theory reference-request elliptic-curves
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
edited Aug 11 at 19:37
YCor
31k4 gold badges95 silver badges147 bronze badges
31k4 gold badges95 silver badges147 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
asked Aug 10 at 13:51
ABarriosABarrios
1237 bronze badges
1237 bronze badges
add a comment |
add a comment |
1 Answer
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$begingroup$
M. Kenku, On the number of $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny class.
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
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$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
add a comment |
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1 Answer
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1 Answer
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oldest
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active
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active
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votes
$begingroup$
M. Kenku, On the number of $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny class.
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
$endgroup$
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
add a comment |
$begingroup$
M. Kenku, On the number of $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny class.
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
$endgroup$
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
add a comment |
$begingroup$
M. Kenku, On the number of $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny class.
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
$endgroup$
M. Kenku, On the number of $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny
class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $mathbfQ$-isomorphism classes of elliptic curves in each $mathbfQ$-isogeny class.
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
edited Aug 11 at 19:38
YCor
31k4 gold badges95 silver badges147 bronze badges
31k4 gold badges95 silver badges147 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
answered Aug 10 at 14:18
Carlo BeenakkerCarlo Beenakker
86.6k9 gold badges208 silver badges314 bronze badges
86.6k9 gold badges208 silver badges314 bronze badges
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
add a comment |
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
$begingroup$
Thank you, Carlo!
$endgroup$
– ABarrios
Aug 10 at 14:21
add a comment |
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