Elliptic curve search results

Results (4 matches)

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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
17.1-a2	17.1-a	$8$	$16$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	17.1	\( 17 \)	\( 17^{8} \)	$0.74813$	$(-2a+1)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$0.758814044$	$2.393455763$	0.440490254	\( -\frac{35937}{83521} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-{x}-14$
272.4-a2	272.4-a	$8$	$16$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	272.4	\( 2^{4} \cdot 17 \)	\( 2^{12} \cdot 17^{8} \)	$1.49625$	$(-a-1), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$2.123938699$	2.060523199	\( -\frac{35937}{83521} \)	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2 a - 1\) , \( 70 a - 126\bigr] \)	${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(2a-1\right){x}+70a-126$
272.5-a2	272.5-a	$8$	$16$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	272.5	\( 2^{4} \cdot 17 \)	\( 2^{12} \cdot 17^{8} \)	$1.49625$	$(-a+2), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{4} \)	$1$	$2.123938699$	2.060523199	\( -\frac{35937}{83521} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -a - 4\) , \( -69 a - 56\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-4\right){x}-69a-56$
289.1-a2	289.1-a	$8$	$16$	\(\Q(\sqrt{17}) \)	$2$	$[2, 0]$	289.1	\( 17^{2} \)	\( 17^{14} \)	$1.51910$	$(-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$16$	\( 2^{2} \)	$1$	$0.580498289$	2.252664248	\( -\frac{35937}{83521} \)	\( \bigl[1\) , \( -1\) , \( 0\) , \( -187 a - 292\) , \( -126667 a - 197799\bigr] \)	${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-187a-292\right){x}-126667a-197799$

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  *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.