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
96.5-c3	96.5-c	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.5	\( 2^{5} \cdot 3 \)	\( 2^{6} \cdot 3^{8} \)	$2.11176$	$(a-4), (4a+13)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{4} \)	$0.676998194$	$12.61917714$	2.263138408	\( \frac{2972645}{81} a + \frac{3418822}{27} \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 528 a - 2257\) , \( -10134 a + 43322\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(528a-2257\right){x}-10134a+43322$
96.5-e3	96.5-e	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.5	\( 2^{5} \cdot 3 \)	\( 2^{6} \cdot 3^{8} \)	$2.11176$	$(a-4), (4a+13)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{2} \)	$2.372205486$	$18.33228224$	2.880059218	\( \frac{2972645}{81} a + \frac{3418822}{27} \)	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -118 a - 391\) , \( 1076 a + 3521\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-118a-391\right){x}+1076a+3521$
192.7-m3	192.7-m	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.7	\( 2^{6} \cdot 3 \)	\( 2^{12} \cdot 3^{8} \)	$2.51132$	$(a-4), (4a+13)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{5} \)	$1.821293637$	$6.488669225$	6.261208549	\( \frac{2972645}{81} a + \frac{3418822}{27} \)	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -5 a - 24\) , \( -54 a - 181\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-24\right){x}-54a-181$
192.7-t3	192.7-t	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.7	\( 2^{6} \cdot 3 \)	\( 2^{12} \cdot 3^{8} \)	$2.51132$	$(a-4), (4a+13)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2Cs	$1$	\( 2^{3} \)	$1$	$17.82632994$	1.180577540	\( \frac{2972645}{81} a + \frac{3418822}{27} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 28003 a - 119690\) , \( -4252968 a + 18181104\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(28003a-119690\right){x}-4252968a+18181104$

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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.