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
686.1-c2	686.1-c	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.1	\( 2 \cdot 7^{3} \)	\( 2^{6} \cdot 7^{3} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B	$1$	\( 2 \)	$0.041738732$	$24.65757654$	1.455474647	\( -\frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -a\) , \( -a\bigr] \)	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}-a{x}-a$
686.1-e2	686.1-e	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	686.1	\( 2 \cdot 7^{3} \)	\( 2^{6} \cdot 7^{9} \)	$1.29349$	$(a), (-2a+1), (2a+1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$					$3$	3B.1.1	$1$	\( 2 \cdot 3^{2} \)	$1$	$3.139999973$	2.220315274	\( -\frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -6 a - 6\) , \( -21 a - 19\bigr] \)	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-6\right){x}-21a-19$
4802.1-ba2	4802.1-ba	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	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	\( -\frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -34 a - 8\) , \( 148 a - 378\bigr] \)	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-34a-8\right){x}+148a-378$
4802.1-bg2	4802.1-bg	$2$	$3$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	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	\( -\frac{208183}{56} a - \frac{292563}{56} \)	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -6 a + 3\) , \( 35 a - 47\bigr] \)	${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a+3\right){x}+35a-47$

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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.