Genus 2 curves in isogeny class 8204.a of discriminant 32816

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
8204.a.32816.1	8204.a	\( 2^{2} \cdot 7 \cdot 293 \)	\( 2^{4} \cdot 7 \cdot 293 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 3 \)	\(0.006769\)	\(18.140318\)	\(0.368388\)	$[72,357,9729,-4102]$	$[72,-22,-3024,-54553,-32816]$	$[-120932352/2051,513216/2051,139968/293]$	$y^2 + y = x^6 - 2x^3 + 2x^2 - x$