Genus 2 curves of conductor 800

Results (3 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
800.a.1600.1	800.a	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{2} \)	$0$	$1$	$\Z/12\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.90.2, 3.2160.21	✓	✓	$1$	\( 3 \)	\(1.000000\)	\(16.770151\)	\(0.349378\)	$[0,84,936,200]$	$[0,-56,832,-784,-1600]$	$[0,-134456/625,728/25]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^4 - x^2$
800.a.8000.1	800.a	\( 2^{5} \cdot 5^{2} \)	\( 2^{6} \cdot 5^{3} \)	$0$	$1$	$\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.4, 3.720.5		✓	$1$	\( 1 \)	\(1.000000\)	\(5.590050\)	\(0.349378\)	$[192,11604,322392,-1000]$	$[192,-6200,142400,-2774800,-8000]$	$[-4076863488/125,27426816/5,-3280896/5]$	$y^2 + (x^3 + x^2 + x + 1)y = -x^6 + 2x^4 + 4x^3 + 2x^2 - 1$
800.a.409600.1	800.a	\( 2^{5} \cdot 5^{2} \)	\( - 2^{14} \cdot 5^{2} \)	$0$	$1$	$\Z/24\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$2$	2.90.3, 3.2160.21	✓	✓	$1$	\( 2^{2} \cdot 3 \)	\(1.000000\)	\(16.770151\)	\(0.349378\)	$[120,309,14889,50]$	$[480,6304,-151552,-28121344,409600]$	$[62208000,1702080,-85248]$	$y^2 = x^6 - 2x^2 + 1$