Genus 2 curves of conductor 187197

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
187197.a.561591.1	187197.a	\( 3 \cdot 23 \cdot 2713 \)	\( - 3^{2} \cdot 23 \cdot 2713 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$4$	$0$	2.20.2	✓	✓	$1$	\( 2 \)	\(0.149512\)	\(7.687663\)	\(2.298797\)	$[134948,-380279,-17099578507,-71883648]$	$[33737,47440227,88975470265,187797575629694,-561591]$	$[-43705118862713991172457/561591,-607218349696938629177/187197,-101270560660423499785/561591]$	$y^2 + (x^3 + x + 1)y = x^6 + 6x^5 - 25x^3 - 3x^2 + 35x - 16$
187197.b.561591.1	187197.b	\( 3 \cdot 23 \cdot 2713 \)	\( - 3^{2} \cdot 23 \cdot 2713 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$0$	2.20.2	✓	✓	$1$	\( 2 \)	\(0.092526\)	\(12.223420\)	\(2.261980\)	$[2524,-282359,-64667061,71883648]$	$[631,28355,-582409,-292876526,561591]$	$[100033806792151/561591,7123898602805/561591,-231892549849/561591]$	$y^2 + (x^3 + x + 1)y = x^6 - 3x^5 - x^4 + 3x^3 - 2x^2 + 2x$