Genus 2 curves of conductor 5414

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
5414.a.10828.1	5414.a	\( 2 \cdot 2707 \)	\( - 2^{2} \cdot 2707 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$12$	$0$		✓	✓	$1$	\( 2 \)	\(0.007352\)	\(20.103606\)	\(0.295620\)	$[108,3993,71523,1385984]$	$[27,-136,300,-2599,10828]$	$[14348907/10828,-669222/2707,54675/2707]$	$y^2 + (x^3 + 1)y = 2x^2 + x$
5414.b.21656.1	5414.b	\( 2 \cdot 2707 \)	\( 2^{3} \cdot 2707 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 3 \)	\(0.009312\)	\(19.003017\)	\(0.530887\)	$[168,660,57273,-86624]$	$[84,184,-2425,-59389,-21656]$	$[-522764928/2707,-13632192/2707,2138850/2707]$	$y^2 + (x^3 + x)y = -x^4 + 2x^2 - 3x + 1$