Genus 2 curve search results

Conductor	Absolute discriminant	Rational points*	Weierstrass points	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

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Results (4 matches)

 

Label	Class	Equation	Sato-Tate	\(\overline{\Q}\)-simple	\(\GL_2\)	Rank*
2916.b.11664.1	2916.b	\(y^2 + y = x^6\)	$D_{3,2}$		✓	$0$
11664.a.11664.1	11664.a	\(y^2 + y = -x^6\)	$D_{6,2}$		✓	$1$
20736.i.373248.1	20736.i	\(y^2 + x^3y = -2\)	$D_{2,1}$		✓	$0$
20736.k.373248.1	20736.k	\(y^2 + x^3y = 2\)	$D_{2,1}$		✓	$1$