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 (displaying both matches)

 

Label	Class	Equation	Sato-Tate	\(\overline{\Q}\)-simple	\(\GL_2\)	Rank*
816.b.52224.1	816.b	\(y^2 + (x^3 + x)y = -x^6 - 12x^4 - 27x^2 - 17\)	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	$0$
1632.a.52224.1	1632.a	\(y^2 + (x^3 + x)y = -x^6 + 11x^4 - 27x^2 + 17\)	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	$0$