Genus 2 curves of conductor 1285

Results (unique match)

 

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
1285.a.1285.1	1285.a	\( 5 \cdot 257 \)	\( 5 \cdot 257 \)	$0$	$0$	$\Z/7\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(24.221343\)	\(0.494313\)	$[56,-1376,-87560,5140]$	$[28,262,7996,38811,1285]$	$[17210368/1285,5751424/1285,6268864/1285]$	$y^2 + y = x^5 - 2x^4 + 3x^3 - x$