LMFDB - Elliptic curves over $\Q(\sqrt{-2}) $ of conductor 1444.2

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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
1444.2-a1	1444.2-a	$1$	$1$	$\Q(\sqrt{-2}) $	$2$	$[0, 1]$	1444.2	$ 2^{2} \cdot 19^{2} $	$ 2^{4} \cdot 19^{2} $	$1.55803$	$(a), (-3a+1), (3a+1)$	0	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓					$1$	$ 1 $	$1$	$4.830783773$	3.415879964	$ -\frac{4194304}{19} $	$ \bigl[0$ , $ -1$ , $ a$ , $ -5$ , $ 7\bigr] $	${y}^2+a{y}={x}^{3}-{x}^{2}-5{x}+7$

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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.