LMFDB - Elliptic curves over $\Q(\sqrt{-349633643}) $

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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{-349633643}) $	$2$	$[0, 1]$	1.0.1	$ 1 $	$ 110977^{12} $	$1670.87962$	$\textsf{none}$		$\mathsf{trivial}$	$\textsf{no}$		$\mathrm{SU}(2)$			✓	✓	$2$	2Cn		$ 1 $	$1$			$ 21867 a + 32123806 $	$ \bigl[1$ , $ a$ , $ a + 1$ , $ 14273482 a - 72324455357$ , $ 2408001869048 a + 509283720941860\bigr] $	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(14273482a-72324455357\right){x}+2408001869048a+509283720941860$

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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.