Genus 2 curves in isogeny class 12800.i of discriminant 819200

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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
12800.i.819200.1	12800.i	\( 2^{9} \cdot 5^{2} \)	\( - 2^{15} \cdot 5^{2} \)	$1$	$2$	$\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.5, 3.360.2	✓	✓	$1$	\( 1 \)	\(0.717386\)	\(6.199040\)	\(1.111776\)	$[520,1141,186367,100]$	$[2080,168096,17260544,1911416576,819200]$	$[47525504000,1846534560,91157248]$	$y^2 = x^6 + 5x^4 + 7x^2 + 2$

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