Genus 2 curves in isogeny class 1269.b of discriminant 102789

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
1269.b.102789.1	1269.b	\( 3^{3} \cdot 47 \)	\( - 3^{7} \cdot 47 \)	$0$	$2$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$0$	$0$	2.15.1			$2$	\( 5 \)	\(1.000000\)	\(4.110305\)	\(0.411030\)	$[91192,19900,603982075,1692]$	$[136788,779593356,5923938871071,50639487394179303,102789]$	$[197075993647247827966976/423,2737061778548953841408/141,152047414479420367856/141]$	$y^2 + (x^3 + x)y = -2x^6 - x^5 - 21x^4 - 8x^3 - 80x^2 - 16x - 103$
1269.b.102789.2	1269.b	\( 3^{3} \cdot 47 \)	\( 3^{7} \cdot 47 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 5 \)	\(1.000000\)	\(8.220609\)	\(0.411030\)	$[80,-140,-1027,1692]$	$[120,810,81,-161595,102789]$	$[102400000/423,640000/47,1600/141]$	$y^2 + xy = x^5 - x^4 + x^2 + x$