Genus 2 curves in isogeny class 1184.a of discriminant 606208

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
1184.a.606208.2	1184.a	\( 2^{5} \cdot 37 \)	\( - 2^{14} \cdot 37 \)	$0$	$1$	$\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$2$	$0$	2.15.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(7.116022\)	\(0.444751\)	$[352,316,34242,74]$	$[1408,79232,5831680,483323904,606208]$	$[337748426752/37,13498597376/37,705633280/37]$	$y^2 = x^6 - 2x^5 + 5x^4 - 4x^3 + 6x^2 - 2x + 2$
1184.a.606208.1	1184.a	\( 2^{5} \cdot 37 \)	\( 2^{14} \cdot 37 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{3} \)	\(1.000000\)	\(14.232044\)	\(0.444751\)	$[176,496,29918,74]$	$[704,15360,140288,-34291712,606208]$	$[10554638336/37,327106560/37,4243712/37]$	$y^2 = 2x^5 + x^4 - 8x^3 - 8x^2 - 2x$