Elliptic curve search results

Base field	Conductor norm	Rank*	Torsion order	CM discriminant
Base field degree/signature	Bad \(p\)	$\Q$-curves	Torsion structure	CM
Analytic order of Ш*	Cyclic isogeny degree	Isogeny class size	Reduction	Galois image
j-invariant	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

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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
1083.1-b1	1083.1-b	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1083.1	\( 3 \cdot 19^{2} \)	\( 3^{2} \cdot 19^{8} \)	$1.77577$	$(a), (19)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	\( 2^{3} \)	$2.601893913$	$2.262154252$	1.699108754	\( \frac{67419143}{390963} \)	\( \bigl[a\) , \( -1\) , \( a\) , \( 7\) , \( -30\bigr] \)	${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+7{x}-30$
1083.1-e1	1083.1-e	$4$	$4$	\(\Q(\sqrt{3}) \)	$2$	$[2, 0]$	1083.1	\( 3 \cdot 19^{2} \)	\( 3^{2} \cdot 19^{8} \)	$1.77577$	$(a), (19)$	$0$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$4$	\( 2^{3} \)	$1$	$4.711524088$	2.720199700	\( \frac{67419143}{390963} \)	\( \bigl[1\) , \( 0\) , \( 1\) , \( 8\) , \( 29\bigr] \)	${y}^2+{x}{y}+{y}={x}^{3}+8{x}+29$

 

  *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.