Genus 2 curves in isogeny class 816.a of discriminant 39168

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
816.a.39168.1	816.a	\( 2^{4} \cdot 3 \cdot 17 \)	\( 2^{8} \cdot 3^{2} \cdot 17 \)	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$6$	$4$	2.360.2, 3.80.1	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(22.166697\)	\(0.307871\)	$[436,3373,434667,4896]$	$[436,5672,77824,439920,39168]$	$[61544958196/153,1836351122/153,57789184/153]$	$y^2 + (x^2 + 1)y = 3x^5 - 4x^3 - x^2 + x$