LMFDB - Elliptic curves over $\Q(\sqrt{-2}) $ of conductor 9.1

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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
9.1-CMa1	9.1-CMa	$1$	$1$	$\Q(\sqrt{-2}) $	$2$	$[0, 1]$	9.1	$ 3^{2} $	$ 3^{6} $	$0.43777$	$(-a-1)$	0	$\Z/6\Z$	$\textsf{yes}$	$-8$	$\mathrm{U}(1)$	✓			✓	$3$	3Cs.1.1	$1$	$ 2 $	$1$	$7.326567372$	0.287814748	$ 8000 $	$ \bigl[a$ , $ -a + 1$ , $ 1$ , $ -1$ , $ 0\bigr] $	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}-{x}$

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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.