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-c4	96.5-c	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.5	\( 2^{5} \cdot 3 \)	\( 2^{12} \cdot 3^{4} \)	$2.11176$	$(a-4), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1.353996389$	$3.154794285$	2.263138408	\( \frac{95313853375}{9} a + \frac{312145070102}{9} \)	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 2328 a - 9952\) , \( 112041 a - 478966\bigr] \)	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2328a-9952\right){x}+112041a-478966$
96.5-e4	96.5-e	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	96.5	\( 2^{5} \cdot 3 \)	\( 2^{12} \cdot 3^{4} \)	$2.11176$	$(a-4), (4a+13)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1.186102743$	$18.33228224$	2.880059218	\( \frac{95313853375}{9} a + \frac{312145070102}{9} \)	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -1918 a - 6286\) , \( 83966 a + 274979\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1918a-6286\right){x}+83966a+274979$
192.7-m4	192.7-m	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.7	\( 2^{6} \cdot 3 \)	\( 2^{6} \cdot 3^{4} \)	$2.51132$	$(a-4), (4a+13)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$3.642587275$	$6.488669225$	6.261208549	\( \frac{95313853375}{9} a + \frac{312145070102}{9} \)	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( -25407 a - 83203\) , \( -4276614 a - 14005555\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-25407a-83203\right){x}-4276614a-14005555$
192.7-t4	192.7-t	$4$	$4$	\(\Q(\sqrt{57}) \)	$2$	$[2, 0]$	192.7	\( 2^{6} \cdot 3 \)	\( 2^{6} \cdot 3^{4} \)	$2.51132$	$(a-4), (4a+13)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2 \)	$1$	$17.82632994$	1.180577540	\( \frac{95313853375}{9} a + \frac{312145070102}{9} \)	\( \bigl[a\) , \( 1\) , \( a\) , \( 44 a - 189\) , \( 335 a - 1433\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(44a-189\right){x}+335a-1433$

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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.