Genus 2 curves in isogeny class 1385.a of discriminant 6925

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
1385.a.6925.1	1385.a	\( 5 \cdot 277 \)	\( 5^{2} \cdot 277 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$9$	$1$	2.6.1	✓	✓	$1$	\( 2 \)	\(0.006508\)	\(16.829506\)	\(0.219038\)	$[56,-2576,-46840,27700]$	$[28,462,1916,-39949,6925]$	$[17210368/6925,10141824/6925,1502144/6925]$	$y^2 + y = x^5 + 3x^4 + 3x^3 - x$