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
135.2-a1	135.2-a	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	135.2	\( 3^{3} \cdot 5 \)	\( 3^{6} \cdot 5^{2} \)	$1.92642$	$(3,a+1), (3,a+2), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \cdot 3 \)	$1$	$5.140502805$	2.438354577	\( \frac{336226}{135} a - \frac{1062059}{135} \)	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 8\) , \( -22 a - 69\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+8{x}-22a-69$
135.2-h1	135.2-h	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	135.2	\( 3^{3} \cdot 5 \)	\( 2^{12} \cdot 3^{6} \cdot 5^{2} \)	$1.92642$	$(3,a+1), (3,a+2), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{2} \)	$1$	$5.140502805$	0.812784859	\( \frac{336226}{135} a - \frac{1062059}{135} \)	\( \bigl[a\) , \( a\) , \( 0\) , \( 7 a + 22\) , \( -154 a - 487\bigr] \)	${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(7a+22\right){x}-154a-487$
405.1-f1	405.1-f	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	405.1	\( 3^{4} \cdot 5 \)	\( 2^{12} \cdot 3^{18} \cdot 5^{2} \)	$2.53532$	$(3,a+1), (3,a+2), (5,a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{3} \)	$1$	$8.581765733$	2.713792606	\( \frac{336226}{135} a - \frac{1062059}{135} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 48 a + 145\) , \( 4480 a + 14165\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(48a+145\right){x}+4480a+14165$
405.1-q1	405.1-q	$2$	$2$	\(\Q(\sqrt{10}) \)	$2$	$[2, 0]$	405.1	\( 3^{4} \cdot 5 \)	\( 3^{18} \cdot 5^{2} \)	$2.53532$	$(3,a+1), (3,a+2), (5,a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$2$	2B	$1$	\( 2^{4} \)	$0.194021615$	$8.581765733$	2.106137702	\( \frac{336226}{135} a - \frac{1062059}{135} \)	\( \bigl[1\) , \( -1\) , \( 1\) , \( 12 a + 37\) , \( 554 a + 1752\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(12a+37\right){x}+554a+1752$

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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.