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

The results below are complete, since the LMFDB contains all elliptic curves with conductor norm at most 50000 over imaginary quadratic fields with absolute discriminant 8

Note: The completeness Only modular elliptic curves are included

Results (unique match)

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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.