LMFDB - Elliptic curve search results

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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

Base change of	Regulator*	Curves per isogeny class	Isogeny class degree	Nonmax$\ \ell$

j-invariant

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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
361.1-a2	361.1-a	$3$	$9$	$\Q(\sqrt{53}) $	$2$	$[2, 0]$	361.1	$ 19^{2} $	$ 19^{6} $	$2.83565$	$(19)$	$1$	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$3$	3Cs.1.1	$1$	$ 3 $	$12.12460493$	$1.848946532$	2.052876179	$ -\frac{89915392}{6859} $	$ \bigl[0$ , $ 1$ , $ 1$ , $ -9$ , $ -15\bigr] $	${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$

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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.

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.