Genus 2 curve search results

Results (displaying both matches)

 

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
810.a.196830.1	810.a	\( 2 \cdot 3^{4} \cdot 5 \)	\( - 2 \cdot 3^{9} \cdot 5 \)	$0$	$1$	$\Z/2\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2$	$C_2$	$1$	$1$	2.60.1, 3.640.4	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(0.328982\)	\(0.328982\)	$[103200,92148840,2874875039973,-3240]$	$[154800,860236740,5905731060081,43549979813677800,-196830]$	$[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$	$y^2 + (x + 1)y = x^5 + 15x^4 + 20x^3 - 297x^2 + 94x - 8$
2430.b.196830.1	2430.b	\( 2 \cdot 3^{5} \cdot 5 \)	\( - 2 \cdot 3^{9} \cdot 5 \)	$0$	$1$	$\Z/6\Z$	\(\mathsf{CM} \times \Q\)	\(\Q \times \Q\)	✓	$N(\mathrm{U}(1)\times\mathrm{SU}(2))$				$C_2$	$C_2$	$1$	$1$	2.60.1, 3.640.2	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(7.089147\)	\(0.787683\)	$[103200,92148840,2874875039973,-3240]$	$[154800,860236740,5905731060081,43549979813677800,-196830]$	$[-451609936896000000000,-16212110811776000000,-2156977131869584000/3]$	$y^2 + xy = 9x^5 - 30x^4 - 30x^3 + 92x^2 + 77x + 15$