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
686.2-c2	686.2-c	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.2	\( 2 \cdot 7^{3} \)	\( 2^{6} \cdot 7^{3} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2 \)	$0.041738732$	$24.65757654$	1.455474647	\( \frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}$
686.2-e2	686.2-e	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.2	\( 2 \cdot 7^{3} \)	\( 2^{6} \cdot 7^{9} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 2 \cdot 3^{2} \)	$1$	$3.139999973$	2.220315274	\( \frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 8 a - 5\) , \( 15 a - 5\bigr] \)	${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-5\right){x}+15a-5$
4802.1-w2	4802.1-w	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	4802.1	\( 2 \cdot 7^{4} \)	\( 2^{6} \cdot 7^{15} \)	$2.10397$	$(a), (-2a+1), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{2} \)	$1.138331575$	$0.760281635$	2.447869585	\( \frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 33 a - 8\) , \( -148 a - 378\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-8\right){x}-148a-378$
4802.1-bd2	4802.1-bd	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	4802.1	\( 2 \cdot 7^{4} \)	\( 2^{6} \cdot 7^{9} \)	$2.10397$	$(a), (-2a+1), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2^{3} \cdot 3 \)	$0.048504617$	$5.970287511$	4.914446106	\( \frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 5 a + 3\) , \( -35 a - 47\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(5a+3\right){x}-35a-47$

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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.