Genus 2 curves in isogeny class 85280.d of discriminant 682240

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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
85280.d.682240.1	85280.d	\( 2^{5} \cdot 5 \cdot 13 \cdot 41 \)	\( 2^{8} \cdot 5 \cdot 13 \cdot 41 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$11$	$1$	2.6.1	✓	✓	$1$	\( 2 \cdot 3 \)	\(0.023037\)	\(12.126018\)	\(1.676109\)	$[74,-392,-5370,-2665]$	$[148,1958,2716,-857949,-682240]$	$[-\frac{277375828}{2665},-\frac{49589287}{5330},-\frac{929551}{10660}]$	$y^2 = x^5 + x^3 - 2x + 1$

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