Genus 2 curves of conductor 6615

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
6615.a.6615.1	6615.a	\( 3^{3} \cdot 5 \cdot 7^{2} \)	\( - 3^{3} \cdot 5 \cdot 7^{2} \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.40.2, 3.40.1	✓	✓	$1$	\( 1 \)	\(0.025778\)	\(23.710626\)	\(0.611220\)	$[540,7497,2428587,846720]$	$[135,447,-16321,-600786,6615]$	$[332150625/49,8146575/49,-2203335/49]$	$y^2 + (x^3 + x^2 + 1)y = -2x^3 - 4x^2 - x + 1$
6615.b.416745.1	6615.b	\( 3^{3} \cdot 5 \cdot 7^{2} \)	\( 3^{5} \cdot 5 \cdot 7^{3} \)	$0$	$3$	$\Z/2\Z\oplus\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$4$	2.360.2	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(6.636255\)	\(0.829532\)	$[5220,347193,554170365,53343360]$	$[1305,56493,2691805,80336619,416745]$	$[3115130754375/343,103335583275/343,11319040025/1029]$	$y^2 + (x^2 + x)y = x^5 - 7x^3 + 10x - 5$