Genus 2 curves of conductor 67006

Results (unique match)

 

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
67006.a.134012.1	67006.a	\( 2 \cdot 33503 \)	\( 2^{2} \cdot 33503 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$18$	$0$		✓	✓	$1$	\( 2 \)	\(0.019104\)	\(19.351847\)	\(0.739388\)	$[372,31641,2506749,17153536]$	$[93,-958,1104,-203773,134012]$	$[6956883693/134012,-385287003/67006,2387124/33503]$	$y^2 + (x^3 + 1)y = 3x^4 + x^3 - x^2$