Genus 2 curves in isogeny class 70450.c of discriminant 704500

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
70450.c.704500.1	70450.c	\( 2 \cdot 5^{2} \cdot 1409 \)	\( - 2^{2} \cdot 5^{3} \cdot 1409 \)	$3$	$4$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$22$	$0$	2.15.1	✓	✓	$1$	\( 2^{2} \)	\(0.046458\)	\(16.521294\)	\(0.767540\)	$[1012,58105,13468045,-90176000]$	$[253,246,20576,1286303,-704500]$	$[-1036579476493/704500,-1991896071/352250,-329262296/176125]$	$y^2 + (x^3 + 1)y = -2x^4 + x^3 + 4x^2 - 3x$