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Genus 2 curves in isogeny class 7680.b of discriminant 46080

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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
7680.b.46080.1	7680.b	$2^{9} \cdot 3 \cdot 5$	$2^{10} \cdot 3^{2} \cdot 5$	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	$\Q$	$\Q$		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$4$	2.360.2	✓	✓	$1$	$2^{2}$	$1.000000$	$17.497219$	$1.093576$	$[200,472,32580,180]$	$[400,5408,56320,-1679616,46080]$	$[2000000000/9,67600000/9,1760000/9]$	$y^2 = x^5 + 3x^4 - 5x^2 - x + 2$

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