Genus 2 curves in isogeny class 2672.a of discriminant 342016

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
2672.a.342016.1	2672.a	\( 2^{4} \cdot 167 \)	\( - 2^{11} \cdot 167 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.10.1	✓	✓	$1$	\( 3^{2} \)	\(0.002591\)	\(18.074641\)	\(0.421450\)	$[276,3129,227757,-42752]$	$[276,1088,6144,128000,-342016]$	$[-1564031349/334,-11169306/167,-228528/167]$	$y^2 + y = x^6 - 6x^4 - 7x^3 - x^2 + x$