Genus 2 curves of conductor 1042

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
1042.a.1042.1	1042.a	\( 2 \cdot 521 \)	\( 2 \cdot 521 \)	$0$	$0$	$\Z/9\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1, 3.80.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(30.423017\)	\(0.375593\)	$[480,3912,728889,-4168]$	$[240,1748,-5521,-1095136,-1042]$	$[-398131200000/521,-12082176000/521,159004800/521]$	$y^2 + (x^3 + x)y = -x^4 - x^3 - x^2 + 2x + 2$