LMFDB - Elliptic curves over $\Q(\sqrt{-10691}) $

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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
1.0.1-a1	1.0.1-a	$1$	$1$	$\Q(\sqrt{-10691}) $	$2$	$[0, 1]$	1.0.1	$ 1 $	$ 179^{12} $	$9.23948$	$\textsf{none}$	$0 \le r \le 1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓	✓	$2$	2Cn		$ 1 $	$1$			$ 55 a - 216 $	$ \bigl[a$ , $ 0$ , $ a + 1$ , $ -41 a + 158813$ , $ 2115 a - 13286543\bigr] $	${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-41a+158813\right){x}+2115a-13286543$

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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.