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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

Galois image	Nonmax$\ \ell$

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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
51035.a.255175.1	51035.a	\( 5 \cdot 59 \cdot 173 \)	\( - 5^{2} \cdot 59 \cdot 173 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$20$	$0$		✓	✓	$1$	\( 2 \)	\(0.014615\)	\(18.563908\)	\(0.542623\)	$[1572,70521,31551645,-32662400]$	$[393,3497,23061,-791509,-255175]$	$[-9374815985193/255175,-212262504129/255175,-3561748389/255175]$	$y^2 + (x^3 + x + 1)y = -3x^4 + 5x^2 + 2x$

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