Genus 2 curves of conductor 960

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
960.a.245760.1	960.a	\( 2^{6} \cdot 3 \cdot 5 \)	\( 2^{14} \cdot 3 \cdot 5 \)	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.180.3, 3.90.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(6.402317\)	\(0.400145\)	$[120,213,10095,30]$	$[480,7328,-15360,-15268096,245760]$	$[103680000,3297600,-14400]$	$y^2 = 2x^5 + x^4 + 4x^3 + x^2 + 2x$
960.a.368640.1	960.a	\( 2^{6} \cdot 3 \cdot 5 \)	\( 2^{13} \cdot 3^{2} \cdot 5 \)	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.180.3, 3.90.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(6.402317\)	\(0.400145\)	$[8952,6072,17987052,1440]$	$[17904,13340192,13237770240,14762078945024,368640]$	$[24952719973569408/5,1038436236963696/5,11510985848256]$	$y^2 = x^5 + 13x^4 + 44x^3 + 13x^2 + x$
960.a.983040.1	960.a	\( 2^{6} \cdot 3 \cdot 5 \)	\( - 2^{16} \cdot 3 \cdot 5 \)	$0$	$2$	$\Z/2\Z\oplus\Z/4\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$2$	$2$	2.180.3, 3.90.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(6.402317\)	\(0.400145\)	$[9,33,666,120]$	$[36,-298,-34260,-330541,983040]$	$[19683/320,-36207/2560,-46251/1024]$	$y^2 = x^5 - 2x^4 - x^3 - 2x^2 + x$