Genus 2 curves of conductor 1600

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
1600.a.409600.1	1600.a	\( 2^{6} \cdot 5^{2} \)	\( 2^{14} \cdot 5^{2} \)	$0$	$1$	$\Z/6\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$0$	2.90.2, 3.2160.21	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(5.702147\)	\(0.475179\)	$[120,309,14889,50]$	$[480,6304,-151552,-28121344,409600]$	$[62208000,1702080,-85248]$	$y^2 = x^6 - 2x^2 - 1$
1600.b.409600.1	1600.b	\( 2^{6} \cdot 5^{2} \)	\( 2^{14} \cdot 5^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/6\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q \times \Q\)	✓	$J(E_1)$				$C_2^2$	$D_4$	$4$	$2$	2.360.1, 3.8640.8	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(12.846191\)	\(0.535258\)	$[248,181,14873,50]$	$[992,39072,1945600,100853504,409600]$	$[58632501248/25,2327987904/25,4674304]$	$y^2 = x^6 - 4x^4 + 4x^2 - 1$