Genus 2 curves of conductor 1142

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
1142.a.2284.1	1142.a	\( 2 \cdot 571 \)	\( - 2^{2} \cdot 571 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(16.871340\)	\(0.337427\)	$[472,-2876,-427657,-9136]$	$[236,2800,46521,784739,-2284]$	$[-183020620544/571,-9200979200/571,-647758404/571]$	$y^2 + (x^3 + x^2)y = -x^4 - x^3 + x^2 - x - 2$
1142.b.9136.1	1142.b	\( 2 \cdot 571 \)	\( - 2^{4} \cdot 571 \)	$0$	$1$	$\Z/12\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3, 3.80.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(17.757282\)	\(0.493258\)	$[864,-4488,-1442025,-36544]$	$[432,8524,257089,9600968,-9136]$	$[-940369969152/571,-42951140352/571,-2998686096/571]$	$y^2 + (x + 1)y = -x^5 + 3x^4 - 6x^2 + x + 3$