Genus 2 curves in isogeny class 16719.a of discriminant 451413

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
16719.a.451413.1	16719.a	\( 3 \cdot 5573 \)	\( - 3^{4} \cdot 5573 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 2^{2} \)	\(0.007582\)	\(16.023546\)	\(0.485972\)	$[100,32713,608309,-57780864]$	$[25,-1337,1053,-440311,-451413]$	$[-9765625/451413,20890625/451413,-8125/5573]$	$y^2 + (x^3 + x + 1)y = -x^4 + 3x^2 - 2x$