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 (6 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
64.4-a2	64.4-a	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	64.4	\( 2^{6} \)	\( 2^{10} \)	$1.04210$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$7.156385278$	0.867839188	\( -\frac{23841914775}{2} a + 30536164178 \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 171 a - 436\) , \( 1835 a - 4700\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(171a-436\right){x}+1835a-4700$
64.4-b2	64.4-b	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	64.4	\( 2^{6} \)	\( 2^{10} \)	$1.04210$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 1 \)	$1$	$28.03945840$	1.700141892	\( -\frac{23841914775}{2} a + 30536164178 \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a - 12\) , \( 3 a + 8\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a-12\right){x}+3a+8$
128.6-a2	128.6-a	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	128.6	\( 2^{7} \)	\( 2^{16} \)	$1.23927$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$4$	\( 2 \)	$1$	$4.411837643$	2.140055600	\( -\frac{23841914775}{2} a + 30536164178 \)	\( \bigl[a\) , \( 1\) , \( a\) , \( -99 a - 157\) , \( -460 a - 721\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-99a-157\right){x}-460a-721$
128.6-d2	128.6-d	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	128.6	\( 2^{7} \)	\( 2^{16} \)	$1.23927$	$(-a+2), (-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$0.327876043$	$17.28603663$	1.374613658	\( -\frac{23841914775}{2} a + 30536164178 \)	\( \bigl[a\) , \( 0\) , \( a\) , \( 31 a - 88\) , \( -142 a + 356\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(31a-88\right){x}-142a+356$
512.1-e2	512.1-e	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	512.1	\( 2^{9} \)	\( 2^{22} \)	$1.75259$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$3.119640315$	1.513247827	\( -\frac{23841914775}{2} a + 30536164178 \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( -768 a - 1200\) , \( -7764 a - 12124\bigr] \)	${y}^2={x}^{3}-{x}^{2}+\left(-768a-1200\right){x}-7764a-12124$
512.1-f2	512.1-f	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	512.1	\( 2^{9} \)	\( 2^{22} \)	$1.75259$	$(-a+2), (-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$0.943323270$	$12.22307372$	2.796510914	\( -\frac{23841914775}{2} a + 30536164178 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 5 a - 60\) , \( -90 a + 144\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(5a-60\right){x}-90a+144$

 

  *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.