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-c1	5324.6-c	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	5324.6	\( 2^{2} \cdot 11^{3} \)	\( 2^{9} \cdot 11^{3} \)	$2.01952$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2 \cdot 7 \)	$0.036077686$	$4.305972120$	3.288129422	\( \frac{399175}{1408} a + \frac{5454499}{1408} \)	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( a + 1\) , \( -a + 3\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+1\right){x}-a+3$
42592.18-k1	42592.18-k	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	42592.18	\( 2^{5} \cdot 11^{3} \)	\( 2^{21} \cdot 11^{9} \)	$3.39641$	$(a), (-a+1), (-2a+3), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \cdot 3 \cdot 7 \)	$0.104477125$	$0.649149721$	8.613037707	\( \frac{399175}{1408} a + \frac{5454499}{1408} \)	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 30 a + 115\) , \( -223 a + 363\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(30a+115\right){x}-223a+363$
42592.6-c1	42592.6-c	$1$	$1$	\(\Q(\sqrt{-7}) \)	$2$	$[0, 1]$	42592.6	\( 2^{5} \cdot 11^{3} \)	\( 2^{21} \cdot 11^{9} \)	$3.39641$	$(a), (-a+1), (-2a+3), (2a+1)$	$0$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$							$1$	\( 2^{2} \)	$1$	$0.649149721$	1.962844260	\( \frac{399175}{1408} a + \frac{5454499}{1408} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -54 a - 89\) , \( -250 a - 123\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-54a-89\right){x}-250a-123$

 

  *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.