Genus 2 curves in isogeny class 2304.a of discriminant 13824

Results (displaying both matches)

 

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
2304.a.13824.2	2304.a	\( 2^{8} \cdot 3^{2} \)	\( - 2^{9} \cdot 3^{3} \)	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$6$	$0$	2.90.6	✓	✓	$1$	\( 2^{2} \)	\(0.099203\)	\(11.872466\)	\(0.294447\)	$[186,54,2664,54]$	$[372,5622,115100,2802579,13824]$	$[515324718,83742501/4,27652775/24]$	$y^2 + (x^3 + x^2 + x + 1)y = x^4 + x^3 + 3x^2 + x + 2$
2304.a.13824.1	2304.a	\( 2^{8} \cdot 3^{2} \)	\( 2^{9} \cdot 3^{3} \)	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$2$	2.180.3	✓	✓	$1$	\( 2^{2} \)	\(0.049602\)	\(23.744931\)	\(0.294447\)	$[102,234,7128,54]$	$[204,1110,4324,-87501,13824]$	$[25557426,2726715/4,312409/24]$	$y^2 + y = 2x^5 + 3x^4 - x^3 - 2x^2$