Genus 2 curves in isogeny class 5170.b of discriminant 10340

Results (unique match)

 

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
5170.b.10340.1	5170.b	\( 2 \cdot 5 \cdot 11 \cdot 47 \)	\( - 2^{2} \cdot 5 \cdot 11 \cdot 47 \)	$2$	$3$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$14$	$0$	2.15.1	✓	✓	$1$	\( 2 \)	\(0.024368\)	\(23.616767\)	\(0.287741\)	$[460,9049,1961635,1323520]$	$[115,174,-11680,-343369,10340]$	$[4022714375/2068,26463225/1034,-7723400/517]$	$y^2 + (x^3 + x^2 + x)y = -2x^2 - x + 1$