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$\ \ell$

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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
6561.1-a2	6561.1-a	$2$	$3$	$\Q(\sqrt{-3}) $	$2$	$[0, 1]$	6561.1	$ 3^{8} $	$ 3^{14} $	$1.39297$	$(-2a+1)$	0	$\Z/3\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓			✓	$2, 3$	2Cn, 3B.1.1[2]	$1$	$ 3 $	$1$	$3.153971350$	1.213964138	$ 33507 a - 45144 $	$ \bigl[1$ , $ -1$ , $ a$ , $ -5 a - 6$ , $ -7 a - 3\bigr] $	${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-5a-6\right){x}-7a-3$

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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.