Genus 2 curves of conductor 1109

Results (3 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
1109.a.1109.1	1109.a	\( 1109 \)	\( 1109 \)	$0$	$0$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.288506\)	\(0.288506\)	$[38880,87301728,855606760992,4436]$	$[19440,1196112,510249312,2122140677184,1109]$	$[2776395315422822400000/1109,8787404722987008000/1109,192830154395443200/1109]$	$y^2 + y = x^5 - 6x^4 - 36x^3 - 6x^2 + 63x - 36$
1109.b.1109.1	1109.b	\( 1109 \)	\( 1109 \)	$0$	$0$	$\Z/7\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,7$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(21.606017\)	\(0.440939\)	$[248,-32,-10424,4436]$	$[124,646,5388,62699,1109]$	$[29316250624/1109,1231679104/1109,82845888/1109]$	$y^2 + y = x^5 - x^4 - x^3 + x^2 + x$
1109.c.1109.1	1109.c	\( 1109 \)	\( 1109 \)	$0$	$0$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(9.552149\)	\(0.382086\)	$[392,292,36703,4436]$	$[196,1552,16001,181873,1109]$	$[289254654976/1109,11685839872/1109,614694416/1109]$	$y^2 + (x^3 + x)y = x^5 - 2x^3 - 2x^2 - 1$