Genus 2 curves of conductor 65520

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
65520.a.65520.1	65520.a	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	$0$	$5$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.6, 3.90.1			$8$	\( 1 \)	\(1.000000\)	\(4.128135\)	\(2.064068\)	$[1573720,96088,50399991420,262080]$	$[786860,25797844802,1127737053817920,55460595434772527999,65520]$	$[3770486200298841428197720000/819,157103494153138593316681400/819,10656851118019203761600]$	$y^2 + (x^3 + x)y = -x^6 - 28x^4 - 336x^2 - 1365$
65520.b.131040.1	65520.b	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	\( - 2^{5} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 13 \)	$1$	$6$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$0$	$0$	2.90.6, 3.90.1			$8$	\( 2 \)	\(0.532647\)	\(3.186150\)	\(1.697092\)	$[3148328,708952,743814934788,524160]$	$[1574164,103249560962,9029520569946240,888368594905774644479,131040]$	$[302064649214662608101539958432/4095,12586012647194024913614166004/4095,170750018582492394877376]$	$y^2 + (x^3 + x)y = -10x^6 - 82x^4 - 227x^2 - 210$