Genus 2 curves of conductor 394

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
394.a.394.1	394.a	\( 2 \cdot 197 \)	\( 2 \cdot 197 \)	$0$	$1$	$\Z/10\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.60.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(20.078274\)	\(0.200783\)	$[11032,106300,393913607,1576]$	$[5516,1250044,371875905,122164372511,394]$	$[12960598758485504,532478222573696,28717744887720]$	$y^2 + (x^3 + x)y = 2x^5 + x^4 - 12x^3 + 17x - 9$
394.a.3152.1	394.a	\( 2 \cdot 197 \)	\( 2^{4} \cdot 197 \)	$0$	$1$	$\Z/20\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$6$	$2$	2.30.3	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(20.078274\)	\(0.200783\)	$[80,-20,649,-12608]$	$[40,70,39,-835,-3152]$	$[-6400000/197,-280000/197,-3900/197]$	$y^2 + (x + 1)y = -x^5$