Genus 2 curves of conductor 70771

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
70771.a.70771.1	70771.a	\( 17 \cdot 23 \cdot 181 \)	\( - 17 \cdot 23 \cdot 181 \)	$0$	$0$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(3.212444\)	\(3.212444\)	$[39988,2027977,27939637061,-9058688]$	$[9997,4079668,2159330736,1235784594392,-70771]$	$[-99850089973004049757/70771,-4075997400200208964/70771,-215803533189816624/70771]$	$y^2 + (x^2 + x + 1)y = x^5 - 10x^4 + 20x^3 + 15x^2 - 1$