Genus 2 curves of conductor 100261

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
100261.a.100261.1	100261.a	\( 7 \cdot 14323 \)	\( - 7 \cdot 14323 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.215449\)	\(6.839751\)	\(1.473618\)	$[7048,-31736,-73311541,-401044]$	$[3524,522730,104271441,23551476296,-100261]$	$[-543474909254042624/100261,-22876265307259520/100261,-1294902814688016/100261]$	$y^2 + (x + 1)y = x^5 - 16x^4 - x^3 + 7x^2 - 3x$
100261.b.100261.1	100261.b	\( 7 \cdot 14323 \)	\( - 7 \cdot 14323 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.095729\)	\(16.886745\)	\(1.616555\)	$[592,-620,494801,401044]$	$[296,3754,-3441,-3777763,100261]$	$[2272262782976/100261,97357497344/100261,-301486656/100261]$	$y^2 + xy = x^5 - x^4 + 3x^2 - 5x + 2$