Genus 2 curves of conductor 7675

Results (displaying both matches)

  Download displayed columns for results to

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
7675.a.7675.1	7675.a	\( 5^{2} \cdot 307 \)	\( - 5^{2} \cdot 307 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(0.118038\)	\(21.445725\)	\(0.632851\)	$[128,304,9815,-30700]$	$[64,120,417,3072,-7675]$	$[-\frac{1073741824}{7675},-\frac{6291456}{1535},-\frac{1708032}{7675}]$	$y^2 + xy = x^5 - 2x^4 + 2x^2 - x$
7675.b.7675.1	7675.b	\( 5^{2} \cdot 307 \)	\( - 5^{2} \cdot 307 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(0.103264\)	\(27.027146\)	\(0.697732\)	$[368,5236,500239,-30700]$	$[184,538,3441,85925,-7675]$	$[-\frac{210906087424}{7675},-\frac{3351473152}{7675},-\frac{116498496}{7675}]$	$y^2 + (x^2 + 1)y = x^5 - 3x^3 + x$

  Download displayed columns for results to