Genus 2 curves in isogeny class 10023.a of discriminant 30069

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
10023.a.30069.1	10023.a	\( 3 \cdot 13 \cdot 257 \)	\( 3^{2} \cdot 13 \cdot 257 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	\( 2 \)	\(0.027384\)	\(11.964997\)	\(0.655295\)	$[280,-2048,-91928,120276]$	$[140,1158,3292,-220021,30069]$	$[53782400000/30069,1059184000/10023,64523200/30069]$	$y^2 + y = x^5 + 2x^4 + x^3 - 2x^2$