Genus 2 curves of conductor 1253

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
1253.a.1253.1	1253.a	\( 7 \cdot 179 \)	\( - 7 \cdot 179 \)	$0$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$3$	✓	✓	$C_2$	$C_2$	$0$	$0$	3.720.5			$2$	\( 1 \)	\(1.000000\)	\(0.207464\)	\(0.414928\)	$[413532,9381037161,999361725629499,160384]$	$[103383,54458647,-97243994481,-3254780028624958,1253]$	$[1687126365978608485162449/179,8596391751971448839127/179,-829487756384515053]$	$y^2 + (x^3 + x^2 + 1)y = -x^6 + 2x^5 - 33x^3 + 43x^2 + 15x - 330$
1253.b.1253.1	1253.b	\( 7 \cdot 179 \)	\( - 7 \cdot 179 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$6$	$0$		✓	✓	$1$	\( 1 \)	\(0.009941\)	\(18.851977\)	\(0.187411\)	$[348,2409,250779,160384]$	$[87,215,467,-1399,1253]$	$[4984209207/1253,141578145/1253,3534723/1253]$	$y^2 + (x^3 + x + 1)y = x^4 + x^2$