Genus 2 curves of conductor 41663

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
41663.a.41663.1	41663.a	\( 61 \cdot 683 \)	\( 61 \cdot 683 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$10$	$0$		✓	✓	$1$	\( 1 \)	\(0.052127\)	\(19.692397\)	\(1.026509\)	$[6628,1297513,2395936453,5332864]$	$[1657,60339,2138465,-24339604,41663]$	$[12491441030500057/41663,274514717773227/41663,5871474288785/41663]$	$y^2 + (x^3 + x + 1)y = x^5 - 5x^4 - 3x^3 + 9x^2 + 3x$
41663.b.41663.1	41663.b	\( 61 \cdot 683 \)	\( 61 \cdot 683 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 1 \)	\(0.022321\)	\(21.884652\)	\(0.488481\)	$[1284,38841,14686365,5332864]$	$[321,2675,16893,-433243,41663]$	$[3408200705601/41663,88478730675/41663,1740671613/41663]$	$y^2 + (x^3 + x + 1)y = x^5 - x^4 - 4x^3 + 2x$