Genus 2 curves in isogeny class 14724.a of discriminant 88344

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
14724.a.88344.1	14724.a	\( 2^{2} \cdot 3^{2} \cdot 409 \)	\( 2^{3} \cdot 3^{3} \cdot 409 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$14$	$0$		✓	✓	$1$	\( 2 \cdot 3 \)	\(0.006321\)	\(16.321469\)	\(0.618998\)	$[132,7569,34137,11308032]$	$[33,-270,2500,2400,88344]$	$[1449459/3272,-179685/1636,75625/2454]$	$y^2 + (x^3 + x + 1)y = -x^5 - x^4 + x^2 - x$