Genus 2 curve search results

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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
35344.a.565504.1	35344.a	\( 2^{4} \cdot 47^{2} \)	\( 2^{8} \cdot 47^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$11$	$1$	2.72.1, 3.432.4	✓	✓	$1$	\( 3^{2} \)	\(0.011293\)	\(11.519297\)	\(1.170768\)	$[58,64,562,-2209]$	$[116,390,5116,110339,-565504]$	$[-\frac{82044596}{2209},-\frac{4755855}{4418},-\frac{1075639}{8836}]$	$y^2 = x^5 - x^4 + x^3 + x^2 - 2x + 1$
565504.a.565504.1	565504.a	\( 2^{8} \cdot 47^{2} \)	\( 2^{8} \cdot 47^{2} \)	$0$	$0$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$1$	$1$	2.72.1, 3.432.4	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(4.366837\)	\(4.366837\)	$[58,64,562,-2209]$	$[116,390,5116,110339,-565504]$	$[-\frac{82044596}{2209},-\frac{4755855}{4418},-\frac{1075639}{8836}]$	$y^2 = x^5 + x^4 + x^3 - x^2 - 2x - 1$

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