Genus 2 curves in isogeny class 5026.a of discriminant 35182

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
5026.a.35182.1	5026.a	\( 2 \cdot 7 \cdot 359 \)	\( 2 \cdot 7^{2} \cdot 359 \)	$2$	$3$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.15.1	✓	✓	$1$	\( 2 \)	\(0.031070\)	\(18.252991\)	\(0.283562\)	$[31220,278329,2852760749,4503296]$	$[7805,2526654,1086135208,523326215681,35182]$	$[591110204777028125/718,12258530733232875/359,675155221982900/359]$	$y^2 + (x^3 + 1)y = 4x^5 + 22x^4 + 46x^3 + 28x^2 + 5x$