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Genus 2 curves in isogeny class 5184.a of discriminant 46656

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Conductor	Absolute discriminant	Rational points*	Weierstrass points	Torsion order

Bad $p$	2-Selmer rank	Analytic rank*	Analytic Ш*	Torsion

$\Q$ -end algebra	$\mathrm{ST}(X)$	$\mathrm{Aut}(X)$	Square Ш*	$\overline{\Q}$ -simple

$\overline{\Q}$ -end algebra	$\mathrm{ST}^0(X)$	$\mathrm{Aut}(X_{\overline{\Q}})$	Locally solvable	$\GL_2$ -type

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Label	Class	Conductor	Discriminant	Rank*	2-Selmer rank	Torsion	$\textrm{End}^0(J_{\overline\Q})$	$\textrm{End}^0(J)$	$\GL_2\textsf{-type}$	Sato-Tate	Nonmaximal primes	$\Q$ -simple	$\overline{\Q}$ -simple	$\Aut(X)$	$\Aut(X_{\overline{\Q}})$	$\Q$ -points	$\Q$ -Weierstrass points	mod- $\ell$ images	Locally solvable	Square Ш*	Analytic Ш*	Tamagawa	Regulator	Real period	Leading coefficient	Igusa-Clebsch invariants	Igusa invariants	G2-invariants	Equation
5184.a.46656.1	5184.a	$2^{6} \cdot 3^{4}$	$- 2^{6} \cdot 3^{6}$	$0$	$1$	$\Z/6\Z$	$\mathrm{M}_2(\mathsf{CM})$	$\mathsf{CM}$	✓	$J(C_2)$		✓		$C_2$	$D_6$	$2$	$0$	2.180.4, 3.8640.16	✓	✓	$1$	$2$	$1.000000$	$14.110203$	$0.783900$	$[76,252,5160,24]$	$[228,654,-644,-143637,46656]$	$[39617584/3,1495262/9,-58121/81]$	$y^2 + x^3y = x^3 + 2$

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