Genus 2 curves of conductor 1643

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
1643.a.1643.1	1643.a	\( 31 \cdot 53 \)	\( - 31 \cdot 53 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.011228\)	\(21.316178\)	\(0.239346\)	$[40,-1088,-3752,6572]$	$[20,198,-572,-12661,1643]$	$[3200000/1643,1584000/1643,-228800/1643]$	$y^2 + y = x^5 + x^4 - 5x^3 + 5x^2 - 2x$