Genus 2 curves in isogeny class 6210.c of discriminant 894240

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
6210.c.894240.1	6210.c	\( 2 \cdot 3^{3} \cdot 5 \cdot 23 \)	\( - 2^{5} \cdot 3^{5} \cdot 5 \cdot 23 \)	$1$	$1$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$5$	✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 3 \cdot 5 \)	\(0.080655\)	\(15.022669\)	\(0.726996\)	$[2604,204561,190462743,114462720]$	$[651,9135,-465361,-96599559,894240]$	$[481170140857/3680,2074317539/736,-21913384129/99360]$	$y^2 + (x^3 + 1)y = x^5 + x^4 + x^3 + 4x^2 - 5x + 1$