Genus 2 curve search results

Conductor	Discriminant	Rational points*	Weierstrass	Torsion order
Bad \(p\)	2-Selmer rank	Analytic rank*	Analytic Ш*	Torsion
\(\Q\)-end algebra	\(\mathrm{ST}(X)\)	\(\mathrm{Aut}(X)\)	Square Ш*	\(\overline{\Q}\)-simple
\(\overline{\Q}\)-end algebra	\(\mathrm{ST}^0(X)\)	\(\mathrm{Aut}(X_{\overline{\Q}})\)	Locally solvable	$\GL_2$-type

Results (3 matches)

 

Label	Class	Equation	Sato-Tate	\(\overline{\Q}\)-simple	\(\GL_2\)	Rank*
4096.b.65536.1	4096.b	\(y^2 = x^5 - x\)	$J(C_2)$		✓	$0$
40000.e.200000.1	40000.e	\(y^2 + x^3y = x^5 - 5x^3 - 10x^2 - 8x - 2\)	$J(C_4)$		✓	$2$
65536.a.65536.1	65536.a	\(y^2 = x^5 + x\)	$D_{2,1}$		✓	$1$