Genus 2 curves in isogeny class 100352.a of discriminant 100352

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
100352.a.100352.1	100352.a	\( 2^{11} \cdot 7^{2} \)	\( 2^{11} \cdot 7^{2} \)	$0$	$1$	$\Z/2\Z$	\(\Q \times \Q\)	\(\Q\)		$N(\mathrm{SU}(2)\times\mathrm{SU}(2))$		✓		$C_2$	$C_2^2$	$2$	$2$	2.90.3, 3.135.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(8.501978\)	\(2.125494\)	$[56,-80,-404,392]$	$[112,736,-512,-149760,100352]$	$[175616,10304,-64]$	$y^2 = x^5 - x^4 + x^2 + x$