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
49.1-a1	49.1-a	$4$	$14$	$\Q(\sqrt{-259}) $	$2$	$[0, 1]$	49.1	$ 7^{2} $	$ 7^{6} $	$3.80485$	$(7,a+3)$	0	$\Z/2\Z$	$\textsf{potential}$	$-7$	$N(\mathrm{U}(1))$	✓	✓		✓	$7$	7B.1.5	$1$	$ 2^{2} $	$1$	$4.944504600$	0.614473133	$ -3375 $	$ \bigl[1$ , $ -1$ , $ 0$ , $ -2$ , $ -1\bigr] $	${y}^2+{x}{y}={x}^3-{x}^2-2{x}-1$

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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.

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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.