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-h2	96.5-h	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.5	\( 2^{5} \cdot 3 \)	\( 2^{12} \cdot 3^{2} \)	$2.11176$	$(a-4), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$0.290302366$	$23.47706964$	1.805456511	\( 150535 a + \frac{1490098}{3} \)	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -214 a - 700\) , \( 2805 a + 9186\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-214a-700\right){x}+2805a+9186$
96.5-i2	96.5-i	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.5	\( 2^{5} \cdot 3 \)	\( 2^{12} \cdot 3^{2} \)	$2.11176$	$(a-4), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$0.664783559$	$13.41811490$	4.726006783	\( 150535 a + \frac{1490098}{3} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 171 a - 740\) , \( -1468 a + 6271\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(171a-740\right){x}-1468a+6271$
192.7-f2	192.7-f	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.7	\( 2^{6} \cdot 3 \)	\( 2^{6} \cdot 3^{2} \)	$2.51132$	$(a-4), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$0.548895963$	$42.11907876$	3.062185337	\( 150535 a + \frac{1490098}{3} \)	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4 a - 7\) , \( 6\bigr] \)	${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(4a-7\right){x}+6$
192.7-v2	192.7-v	$2$	$2$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.7	\( 2^{6} \cdot 3 \)	\( 2^{6} \cdot 3^{2} \)	$2.51132$	$(a-4), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$14.95844768$	0.990647398	\( 150535 a + \frac{1490098}{3} \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2867 a - 9381\) , \( -161465 a - 528780\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2867a-9381\right){x}-161465a-528780$

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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.