Elliptic curve search results

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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Results (3 matches)

 

Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
5324.6-a1	5324.6-a	$2$	$3$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	5324.6	\( 2^{2} \cdot 11^{3} \)	\( 2^{13} \cdot 11^{11} \)	$2.01952$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 2 \cdot 3^{2} \)	$0.804718677$	$0.722336016$	1.757617297	\( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \)	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -45 a + 7\) , \( -280 a + 120\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-45a+7\right){x}-280a+120$
42592.18-c2	42592.18-c	$2$	$3$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	42592.18	\( 2^{5} \cdot 11^{3} \)	\( 2^{25} \cdot 11^{5} \)	$3.39641$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{2} \)	$0.489938282$	$1.197858769$	3.549097701	\( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \)	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 17 a - 6\) , \( -14 a - 68\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-6\right){x}-14a-68$
42592.6-d2	42592.6-d	$2$	$3$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	42592.6	\( 2^{5} \cdot 11^{3} \)	\( 2^{25} \cdot 11^{5} \)	$3.39641$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{3} \cdot 3 \cdot 5 \)	$0.034494406$	$1.197858769$	7.496292234	\( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \)	\( \bigl[a\) , \( a\) , \( a\) , \( -17 a + 12\) , \( 52 a - 49\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-17a+12\right){x}+52a-49$

 

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.