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 (5 matches)

 

Label	Class	Equation	Sato-Tate	\(\overline{\Q}\)-simple	\(\GL_2\)	Rank*
3125.a.3125.1	3125.a	\(y^2 + y = x^5\)	$F_{ac}$	✓		$0$
10000.b.800000.1	10000.b	\(y^2 = x^5 + 1\)	$F_{ac}$	✓		$0$
50000.a.200000.1	50000.a	\(y^2 + y = 2x^5\)	$F_{ac}$	✓		$1$
50625.a.253125.1	50625.a	\(y^2 + y = x^5 - 1\)	$F_{ac}$	✓		$1$
160000.c.800000.1	160000.c	\(y^2 = x^5 - 1\)	$F_{ac}$	✓		$1$