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
1152.1-a1	1152.1-a	$2$	$2$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1152.1	\( 2^{7} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{4} \)	$1.47247$	$(a), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$0.370855344$	$8.585176139$	2.251327905	\( \frac{4000}{9} \)	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 6\) , \( -10 a + 14\bigr] \)	${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+6\right){x}-10a+14$
1152.1-d1	1152.1-d	$2$	$2$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1152.1	\( 2^{7} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{4} \)	$1.47247$	$(a), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	\( 2^{2} \)	$0.370855344$	$8.585176139$	2.251327905	\( \frac{4000}{9} \)	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 6\) , \( 10 a + 14\bigr] \)	${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+6\right){x}+10a+14$
2304.1-b1	2304.1-b	$2$	$2$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	2304.1	\( 2^{8} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{4} \)	$1.75107$	$(a), (3)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$0.319732820$	$11.50728806$	2.601628048	\( \frac{4000}{9} \)	\( \bigl[0\) , \( 1\) , \( 0\) , \( 2\) , \( 2\bigr] \)	${y}^2={x}^{3}+{x}^{2}+2{x}+2$
2304.1-n1	2304.1-n	$2$	$2$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	2304.1	\( 2^{8} \cdot 3^{2} \)	\( 2^{14} \cdot 3^{4} \)	$1.75107$	$(a), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	\( 2^{2} \)	$1$	$6.405092923$	2.264542320	\( \frac{4000}{9} \)	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2\) , \( -2\bigr] \)	${y}^2={x}^{3}-{x}^{2}+2{x}-2$

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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.