Genus 2 curves of conductor 909

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
909.a.909.1	909.a	\( 3^{2} \cdot 101 \)	\( 3^{2} \cdot 101 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$2$	2.30.3	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(21.805548\)	\(0.340712\)	$[40,-200,-5469,3636]$	$[20,50,441,1580,909]$	$[3200000/909,400000/909,19600/101]$	$y^2 + (x^3 + x)y = -x^4 + x^2 - x$
909.a.8181.1	909.a	\( 3^{2} \cdot 101 \)	\( 3^{4} \cdot 101 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(21.805548\)	\(0.340712\)	$[1384,44560,19431635,32724]$	$[692,12526,35569,-33071732,8181]$	$[158683025503232/8181,4150789321088/8181,17032713616/8181]$	$y^2 + xy = 3x^5 - 7x^4 + x^3 + 6x^2 - 3x$