Genus 2 curves in isogeny class 200704.d of discriminant 401408

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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
200704.d.401408.1	200704.d	\( 2^{12} \cdot 7^{2} \)	\( 2^{13} \cdot 7^{2} \)	$2$	$3$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.120.5	✓	✓	$1$	\( 2 \)	\(0.336432\)	\(16.214168\)	\(2.727484\)	$[451,1330,187628,49]$	$[1804,121414,10025348,836092099,401408]$	$[\frac{18658757027251}{392},\frac{5568886892657}{3136},\frac{509791452137}{6272}]$	$y^2 = 2x^5 + 6x^4 - 9x^3 - x^2 + 4x - 1$

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