LMFDB - Elliptic curves over $\Q(\sqrt{-1}) $ of conductor 169.3

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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
169.3-CMa1	169.3-CMa	$1$	$1$	$\Q(\sqrt{-1}) $	$2$	$[0, 1]$	169.3	$ 13^{2} $	$ 13^{9} $	$0.64438$	$(2a+3)$	0	$\Z/2\Z$	$\textsf{yes}$	$-4$	$\mathrm{U}(1)$	✓			✓	$13$	13Cs.3.1	$1$	$ 2 $	$1$	$2.008431027$	1.004215513	$ 1728 $	$ \bigl[i + 1$ , $ i$ , $ i$ , $ -12 i + 2$ , $ i + 6\bigr] $	${y}^2+\left(i+1\right){x}{y}+i{y}={x}^{3}+i{x}^{2}+\left(-12i+2\right){x}+i+6$

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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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