Elliptic curve search results

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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
1568.1-c2	1568.1-c	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1568.1	\( 2^{5} \cdot 7^{2} \)	\( 2^{6} \cdot 7^{4} \)	$1.59045$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$0.393548229$	$16.88594825$	2.349516090	\( \frac{125000}{49} \)	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2\) , \( -1\bigr] \)	${y}^2+a{x}{y}={x}^{3}-2{x}-1$
1568.1-d2	1568.1-d	$4$	$4$	\(\Q(\sqrt{2}) \)	$2$	$[2, 0]$	1568.1	\( 2^{5} \cdot 7^{2} \)	\( 2^{6} \cdot 7^{4} \)	$1.59045$	$(a), (-2a+1), (2a+1)$	$1$	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2Cs	$1$	\( 2^{3} \)	$0.306002722$	$23.59896529$	2.553131942	\( \frac{125000}{49} \)	\( \bigl[a\) , \( -1\) , \( 0\) , \( -2\) , \( 1\bigr] \)	${y}^2+a{x}{y}={x}^{3}-{x}^{2}-2{x}+1$

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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.