Genus 2 curves of conductor 1127

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
1127.a.1127.1	1127.a	\( 7^{2} \cdot 23 \)	\( - 7^{2} \cdot 23 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$8$	$0$	2.40.2	✓	✓	$1$	\( 1 \)	\(0.006656\)	\(25.743921\)	\(0.171351\)	$[60,105,37947,144256]$	$[15,5,-501,-1885,1127]$	$[759375/1127,16875/1127,-112725/1127]$	$y^2 + (x^3 + x + 1)y = -x^4 + x^3 - x^2 - x$