Genus 2 curves in isogeny class 18624.b of discriminant 446976

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
18624.b.446976.1	18624.b	\( 2^{6} \cdot 3 \cdot 97 \)	\( - 2^{9} \cdot 3^{2} \cdot 97 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$14$	$0$	2.10.1	✓	✓	$1$	\( 2^{3} \)	\(0.005490\)	\(16.051741\)	\(0.704939\)	$[52,2809,60767,55872]$	$[52,-1760,-26640,-1120720,446976]$	$[742586/873,-483340/873,-31265/194]$	$y^2 + (x^3 + x)y = -x^4 + 4x^2 - 4x + 1$