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

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
11.1-a3	11.1-a	$3$	$25$	$\Q(\zeta_{11})^+$	$5$	$[5, 0]$	11.1	$ 11 $	$ - 11^{5} $	$13.74242$	$(a^2+a-2)$	0	$\Z/25\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$5$	5B.1.1	$1$	$ 5 $	$1$	$10292.39055$	0.680488632	$ -\frac{4096}{11} $	$ \bigl[0$ , $ -1$ , $ 1$ , $ 0$ , $ 0\bigr] $	${y}^2+{y}={x}^{3}-{x}^{2}$

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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.