LMFDB - Elliptic curves over $\Q(\sqrt{-31}) $ of conductor 32.3

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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
32.3-a1	32.3-a	$1$	$1$	$\Q(\sqrt{-31}) $	$2$	$[0, 1]$	32.3	$ 2^{5} $	$ 2^{20} $	$1.18333$	$(2,a), (2,a+1)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$				✓	$2, 5$	2Cn, 5S4	$1$	$ 2 $	$0.139158379$	$8.191609121$	1.637901283	$ 1536 a + 1280 $	$ \bigl[0$ , $ -1$ , $ 0$ , $ -a + 3$ , $ -3\bigr] $	${y}^2={x}^3-{x}^2+\left(-a+3\right){x}-3$

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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.