Genus 2 curves in isogeny class 3138.a of discriminant 301248

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
3138.a.301248.1	3138.a	\( 2 \cdot 3 \cdot 523 \)	\( - 2^{6} \cdot 3^{2} \cdot 523 \)	$1$	$2$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$2$	2.30.3	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(0.009642\)	\(13.716170\)	\(0.396771\)	$[296,-1820,-2495,1204992]$	$[148,1216,-4689,-543157,301248]$	$[1109503312/4707,61594048/4707,-713249/2092]$	$y^2 + (x^3 + x)y = -x^4 - 2x^2 - x + 1$