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
50625.1-CMa1	50625.1-CMa	$1$	$1$	$\Q(\sqrt{-3}) $	$2$	$[0, 1]$	50625.1	$ 3^{4} \cdot 5^{4} $	$ 3^{6} \cdot 5^{8} $	$2.32162$	$(-2a+1), (5)$	0	$\Z/3\Z$	$\textsf{yes}$	$-3$	$\mathrm{U}(1)$	✓	✓		✓	$3$	3B.1.1[2]	$1$	$ 3 $	$1$	$2.773111858$	1.067371251	$ 0 $	$ \bigl[0$ , $ 0$ , $ 1$ , $ 0$ , $ 6\bigr] $	${y}^2+{y}={x}^{3}+6$

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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.