Genus 2 curves of conductor 1532

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
1532.a.1532.1	1532.a	\( 2^{2} \cdot 383 \)	\( 2^{2} \cdot 383 \)	$0$	$0$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(12.961311\)	\(0.518452\)	$[372,2673,322425,196096]$	$[93,249,261,-9432,1532]$	$[6956883693/1532,200284893/1532,2257389/1532]$	$y^2 + (x^3 + 1)y = -x - 1$
1532.a.392192.1	1532.a	\( 2^{2} \cdot 383 \)	\( 2^{10} \cdot 383 \)	$0$	$0$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.518452\)	\(0.518452\)	$[52500,33335793,517241464281,50200576]$	$[13125,5788743,3113886477,1840053622644,392192]$	$[389490222930908203125/392192,13088268780029296875/392192,536415600139453125/392192]$	$y^2 + (x^2 + x + 1)y = x^5 + 7x^4 - 53x^2 + 12x - 1$