Genus 2 curves in isogeny class 12700.a of discriminant 25400

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
12700.a.25400.1	12700.a	\( 2^{2} \cdot 5^{2} \cdot 127 \)	\( 2^{3} \cdot 5^{2} \cdot 127 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$3$	✓	✓	$C_2$	$C_2$	$14$	$0$	3.40.1	✓	✓	$1$	\( 3 \)	\(0.008095\)	\(22.455917\)	\(0.545362\)	$[708,14865,2575065,3251200]$	$[177,686,7524,215288,25400]$	$[173726604657/25400,1902014919/12700,58929849/6350]$	$y^2 + (x^3 + x + 1)y = x^5 - 3x^3 - x^2 + x$