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
2450.1-i2	2450.1-i	$6$	$8$	$\Q(\sqrt{2}) $	$2$	$[2, 0]$	2450.1	$ 2 \cdot 5^{2} \cdot 7^{2} $	$ 2^{8} \cdot 5^{4} \cdot 7^{2} $	$1.77818$	$(a), (-2a+1), (2a+1), (5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$ 2^{4} $	$1$	$5.572473402$	1.970166865	$ \frac{1367631}{2800} $	$ \bigl[1$ , $ -1$ , $ 1$ , $ 2$ , $ -3\bigr] $	${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}-3$

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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.