Genus 2 curves of conductor 10609

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
10609.a.10609.1	10609.a	\( 103^{2} \)	\( 103^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$8$	$0$	2.12.2, 3.2160.18	✓	✓	$1$	\( 1 \)	\(0.022299\)	\(16.854924\)	\(0.375850\)	$[188,3721,160523,-1357952]$	$[47,-63,35,-581,-10609]$	$[-229345007/10609,6540849/10609,-77315/10609]$	$y^2 + (x^3 + x + 1)y = x^2 + x$
10609.b.10609.1	10609.b	\( 103^{2} \)	\( 103^{2} \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.2.1	✓	✓	$1$	\( 1 \)	\(0.033273\)	\(23.052961\)	\(0.767044\)	$[1092,41097,8454549,1357952]$	$[273,1393,59529,3577742,10609]$	$[1516398112593/10609,28342558881/10609,4436636841/10609]$	$y^2 + (x^3 + x + 1)y = -3x^4 + 5x^2 - 5x + 1$