Genus 2 curves in isogeny class 464.a of discriminant 29696

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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
464.a.29696.1	464.a	\( 2^{4} \cdot 29 \)	\( - 2^{10} \cdot 29 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(14.421431\)	\(0.225335\)	$[680,-5255,-1253953,-3712]$	$[680,22770,1180736,71106895,-29696]$	$[-\frac{141985700000}{29},-\frac{6991813125}{29},-\frac{533176100}{29}]$	$y^2 + (x + 1)y = 8x^5 + 3x^4 - 4x^3 - 2x^2$
464.a.29696.2	464.a	\( 2^{4} \cdot 29 \)	\( - 2^{10} \cdot 29 \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$3$	2.120.3	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(1.802679\)	\(0.225335\)	$[45368,202225,3012190355,-3712]$	$[45368,85625826,215176422416,607585463496703,-29696]$	$[-\frac{187693059992988715232}{29},-\frac{7808250185554819143}{29},-\frac{432507850151022641}{29}]$	$y^2 + xy = 4x^5 + 33x^4 + 72x^3 + 16x^2 + x$

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