Genus 2 curves of conductor 1125

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
1125.a.151875.1	1125.a	\( 3^{2} \cdot 5^{3} \)	\( - 3^{5} \cdot 5^{4} \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2$	$C_2$	$3$	$3$	2.120.3, 3.80.4	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(1.964402\)	\(0.491100\)	$[8600,612100,1556297975,-607500]$	$[4300,668400,132975225,31258726875,-151875]$	$[-2352135088000000/243,-28342655360000/81,-437104339600/27]$	$y^2 + xy = 15x^5 + 50x^4 + 55x^3 + 22x^2 + 3x$