Genus 2 curves of conductor 4925

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
4925.a.4925.1	4925.a	\( 5^{2} \cdot 197 \)	\( 5^{2} \cdot 197 \)	$0$	$2$	$\Z/7\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$7$	✓	✓	$C_2$	$C_2$	$0$	$0$		✓	✓	$4$	\( 1 \)	\(1.000000\)	\(11.441716\)	\(0.934018\)	$[15856,1060,5493640,19700]$	$[7928,2618706,1153250976,571338155823,4925]$	$[31319744274299322368/4925,1304901311754918912/4925,72485495792707584/4925]$	$y^2 + y = 5x^6 - 5x^5 + 12x^3 + 2x^2 - 5x - 2$
4925.b.4925.1	4925.b	\( 5^{2} \cdot 197 \)	\( 5^{2} \cdot 197 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$3$	✓	✓	$C_2$	$C_2$	$12$	$0$	3.40.1	✓	✓	$1$	\( 1 \)	\(0.012038\)	\(23.181407\)	\(0.279065\)	$[216,1140,86400,-19700]$	$[108,296,-984,-48472,-4925]$	$[-14693280768/4925,-372874752/4925,11477376/4925]$	$y^2 + x^3y = -x^4 - x^3 + x + 1$