Genus 2 curves of conductor 523

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
523.a.523.1	523.a	\( 523 \)	\( -523 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(24.819904\)	\(0.248199\)	$[120,-540,-29169,-2092]$	$[60,240,2241,19215,-523]$	$[-777600000/523,-51840000/523,-8067600/523]$	$y^2 + (x + 1)y = x^5 - x^4 - x^3$
523.a.523.2	523.a	\( 523 \)	\( -523 \)	$0$	$1$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$2$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.992796\)	\(0.248199\)	$[332400,10084860,1107044456391,-2092]$	$[166200,1149254190,10581558955401,109467476288772525,-523]$	$[-126810465636208320000000000/523,-5276053055713522320000000/523,-292288477352026798440000/523]$	$y^2 + xy = x^5 - 31x^4 - 110x^3 + 21x^2 - x$