Elliptic curve search results

Results (3 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
49.2-a2	49.2-a	$2$	$2$	3.3.361.1	$3$	$[3, 0]$	49.2	\( 7^{2} \)	\( - 7^{6} \)	$3.24782$	$(-a), (a^2+a-5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	\( 2^{2} \)	$1$	$32.40792394$	1.705680207	\( \frac{386002347110}{2401} a^{2} + \frac{496019123941}{2401} a - \frac{1182368108178}{2401} \)	\( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{2} + a - 3\) , \( -6 a^{2} - 4 a + 29\) , \( 18 a^{2} - 6 a - 128\bigr] \)	${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+\left(-6a^{2}-4a+29\right){x}+18a^{2}-6a-128$
343.3-b2	343.3-b	$2$	$2$	3.3.361.1	$3$	$[3, 0]$	343.3	\( 7^{3} \)	\( - 7^{12} \)	$4.49201$	$(-a), (a^2+a-5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$6.854272287$	0.721502346	\( \frac{386002347110}{2401} a^{2} + \frac{496019123941}{2401} a - \frac{1182368108178}{2401} \)	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -20 a^{2} - 22 a + 75\) , \( -6 a^{2} - 55 a - 101\bigr] \)	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a^{2}-22a+75\right){x}-6a^{2}-55a-101$
343.6-f2	343.6-f	$2$	$2$	3.3.361.1	$3$	$[3, 0]$	343.6	\( 7^{3} \)	\( - 7^{12} \)	$4.49201$	$(-a), (a^2+a-5)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$0.134750157$	$40.01100224$	3.405150844	\( \frac{386002347110}{2401} a^{2} + \frac{496019123941}{2401} a - \frac{1182368108178}{2401} \)	\( \bigl[a^{2} + a - 3\) , \( -a^{2} + 3\) , \( a^{2} - 3\) , \( -54 a^{2} - 48 a + 140\) , \( 271 a^{2} + 252 a - 713\bigr] \)	${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-54a^{2}-48a+140\right){x}+271a^{2}+252a-713$

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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.