Genus 2 curves in isogeny class 1280.a of discriminant 12800

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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
1280.a.12800.1	1280.a	\( 2^{8} \cdot 5 \)	\( - 2^{9} \cdot 5^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.180.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(17.070788\)	\(0.474189\)	$[22,-170,-1832,-50]$	$[44,534,7684,13235,-12800]$	$[-\frac{322102}{25},-\frac{355377}{100},-\frac{232441}{200}]$	$y^2 + y = 2x^5 + x^4 - x^3 - x^2$

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