Genus 2 curves in isogeny class 1637.a of discriminant 1637

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
1637.a.1637.1	1637.a	\( 1637 \)	\( 1637 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.012103\)	\(20.489120\)	\(0.247972\)	$[40,-800,-7256,-6548]$	$[20,150,84,-5205,-1637]$	$[-3200000/1637,-1200000/1637,-33600/1637]$	$y^2 + y = x^5 - x^4 + x^3 - x^2$