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
3564.2-a1	3564.2-a	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	3564.2	\( 2^{2} \cdot 3^{4} \cdot 11 \)	\( 2^{8} \cdot 3^{12} \cdot 11^{9} \)	$2.28991$	$(-a), (a-1), (-2a+1), (2)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.2	$9$	\( 2^{2} \)	$1$	$0.209915802$	4.557023695	\( -\frac{44349865310515}{7730448} a - \frac{78923474734103}{2576816} \)	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 1196 a - 5867\) , \( -52290 a + 164867\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1196a-5867\right){x}-52290a+164867$
10692.3-a1	10692.3-a	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	10692.3	\( 2^{2} \cdot 3^{5} \cdot 11 \)	\( 2^{8} \cdot 3^{12} \cdot 11^{9} \)	$3.01370$	$(-a), (a-1), (-2a+1), (2)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 2^{4} \cdot 3^{2} \)	$0.758463233$	$0.209915802$	3.072297712	\( -\frac{44349865310515}{7730448} a - \frac{78923474734103}{2576816} \)	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -2463 a - 2645\) , \( 91888 a + 13579\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-2463a-2645\right){x}+91888a+13579$
39204.2-b1	39204.2-b	$3$	$9$	\(\Q(\sqrt{-11}) \)	$2$	$[0, 1]$	39204.2	\( 2^{2} \cdot 3^{4} \cdot 11^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 11^{15} \)	$4.17030$	$(-a), (a-1), (-2a+1), (2)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{4} \cdot 3 \)	$0.844567023$	$0.109624952$	5.359798024	\( -\frac{44349865310515}{7730448} a - \frac{78923474734103}{2576816} \)	\( \bigl[a\) , \( a\) , \( a\) , \( -2782 a - 18726\) , \( -236524 a - 954375\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-2782a-18726\right){x}-236524a-954375$

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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.