Genus 2 curves of conductor 48841

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
48841.a.48841.1	48841.a	\( 13^{2} \cdot 17^{2} \)	\( 13^{2} \cdot 17^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$6$	$0$	2.12.2, 3.432.4	✓	✓	$1$	\( 1 \)	\(0.064288\)	\(15.225850\)	\(0.978843\)	$[188,625,108023,-6251648]$	$[47,66,-920,-11899,-48841]$	$[-229345007/48841,-6852318/48841,2032280/48841]$	$y^2 + (x^3 + x + 1)y = x^5 + x^3 - x$
48841.b.830297.1	48841.b	\( 13^{2} \cdot 17^{2} \)	\( - 13^{2} \cdot 17^{3} \)	$0$	$0$	$\mathsf{trivial}$	\(\mathrm{M}_2(\Q)\)	\(\mathsf{CM}\)	✓	$E_6$		✓		$C_6$	$D_6$	$0$	$0$	2.40.3, 3.480.12		✓	$1$	\( 1 \)	\(1.000000\)	\(4.401272\)	\(4.401272\)	$[764,10777,650195,106278016]$	$[191,1071,30923,1189813,830297]$	$[254194901951/830297,438975873/48841,3903467/2873]$	$y^2 + (x^3 + x + 1)y = -x^6 + 2x^5 - 5x^4 + 6x^3 - 6x^2 + 2x - 1$