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-a4	64.4-a	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	64.4	\( 2^{6} \)	\( 2^{13} \)	$1.04210$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$7.156385278$	0.867839188	\( \frac{1592342311}{2} a + 1243265046 \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 16 a - 41\) , \( 4 a - 13\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(16a-41\right){x}+4a-13$
64.4-b4	64.4-b	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	64.4	\( 2^{6} \)	\( 2^{13} \)	$1.04210$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$7.009864600$	1.700141892	\( \frac{1592342311}{2} a + 1243265046 \)	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -38 a - 57\) , \( -180 a - 281\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a-57\right){x}-180a-281$
128.6-a4	128.6-a	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	128.6	\( 2^{7} \)	\( 2^{7} \)	$1.23927$	$(-a+2), (-a-1)$	$0$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 1 \)	$1$	$35.29470114$	2.140055600	\( \frac{1592342311}{2} a + 1243265046 \)	\( \bigl[a\) , \( -1\) , \( a\) , \( -a - 8\) , \( a + 2\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-8\right){x}+a+2$
128.6-d4	128.6-d	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	128.6	\( 2^{7} \)	\( 2^{7} \)	$1.23927$	$(-a+2), (-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 1 \)	$0.327876043$	$34.57207326$	1.374613658	\( \frac{1592342311}{2} a + 1243265046 \)	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 83 a - 216\) , \( 136 a - 350\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(83a-216\right){x}+136a-350$
512.1-e4	512.1-e	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	512.1	\( 2^{9} \)	\( 2^{25} \)	$1.75259$	$(-a+2), (-a-1)$	$0$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$12.47856126$	1.513247827	\( \frac{1592342311}{2} a + 1243265046 \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 106 a - 273\) , \( -87 a + 223\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(106a-273\right){x}-87a+223$
512.1-f4	512.1-f	$4$	$4$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	512.1	\( 2^{9} \)	\( 2^{25} \)	$1.75259$	$(-a+2), (-a-1)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.235830817$	$12.22307372$	2.796510914	\( \frac{1592342311}{2} a + 1243265046 \)	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -90 a - 145\) , \( 633 a + 993\bigr] \)	${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-90a-145\right){x}+633a+993$

 

  *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.