Genus 2 curves in isogeny class 10121.a of discriminant 293509

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
10121.a.293509.1	10121.a	\( 29 \cdot 349 \)	\( 29^{2} \cdot 349 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	\( 2 \)	\(0.042928\)	\(10.777185\)	\(0.925276\)	$[640,-512,-234048,1174036]$	$[320,4352,94272,2806784,293509]$	$[3355443200000/293509,142606336000/293509,9653452800/293509]$	$y^2 + y = x^5 + 2x^4 + 4x + 3$