Genus 2 curves in isogeny class 1122.a of discriminant 1122

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
1122.a.1122.1	1122.a	\( 2 \cdot 3 \cdot 11 \cdot 17 \)	\( 2 \cdot 3 \cdot 11 \cdot 17 \)	$0$	$2$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.180.3, 3.90.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(6.820719\)	\(0.426295\)	$[56004,288321,5331417537,143616]$	$[14001,8155820,6325887612,5512838145803,1122]$	$[179338702480653356667/374,3730727674118765970/187,1105214886926046]$	$y^2 + (x^2 + x)y = x^5 + 7x^4 - 43x^2 + 51x - 17$