Genus 2 curves of conductor 45413

Results (displaying both matches)

 

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
45413.a.45413.1	45413.a	\( 45413 \)	\( -45413 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 1 \)	\(0.025475\)	\(19.997449\)	\(0.509438\)	$[548,9193,955301,-5812864]$	$[137,399,7261,208889,-45413]$	$[-48261724457/45413,-1025969847/45413,-136281709/45413]$	$y^2 + (x^3 + x + 1)y = -x^5 + 2x^2 - 3x$
45413.b.45413.1	45413.b	\( 45413 \)	\( -45413 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.138561\)	\(17.384758\)	\(2.408846\)	$[16,-4580,605321,181652]$	$[8,766,-68953,-284595,45413]$	$[32768/45413,392192/45413,-4412992/45413]$	$y^2 + xy = x^5 - 3x^4 + 2x^3 - x + 2$