LMFDB - Elliptic curves over $\Q(\sqrt{-7}) $ of conductor 1225.1

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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
1225.1-a1	1225.1-a	$1$	$1$	$\Q(\sqrt{-7}) $	$2$	$[0, 1]$	1225.1	$ 5^{2} \cdot 7^{2} $	$ 5^{6} \cdot 7^{6} $	$1.39869$	$(-2a+1), (5)$	$1$	$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$3$	3Cn	$1$	$ 2 \cdot 3 $	$0.032236886$	$2.301409224$	0.672990855	$ -\frac{110592}{125} $	$ \bigl[0$ , $ 0$ , $ 1$ , $ -7$ , $ 12\bigr] $	${y}^2+{y}={x}^{3}-7{x}+12$

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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.