Genus 2 curves of conductor 1706

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
1706.a.3412.1	1706.a	\( 2 \cdot 853 \)	\( 2^{2} \cdot 853 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 2 \)	\(0.005601\)	\(25.509541\)	\(0.285782\)	$[304,1816,196969,-13648]$	$[152,660,-977,-146026,-3412]$	$[-20284203008/853,-579448320/853,5643152/853]$	$y^2 + (x + 1)y = x^6 - x^5 - x^4$