Genus 2 curves of conductor 450

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
450.a.2700.1	450.a	\( 2 \cdot 3^{2} \cdot 5^{2} \)	\( - 2^{2} \cdot 3^{3} \cdot 5^{2} \)	$0$	$1$	$\Z/24\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$6$	$0$	2.180.4, 3.720.4	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(18.778996\)	\(0.195615\)	$[364,3529,393211,345600]$	$[91,198,0,-9801,2700]$	$[6240321451/2700,8289281/150,0]$	$y^2 + (x^3 + 1)y = x^5 + 3x^4 + 3x^3 + 3x^2 + x$
450.a.36450.1	450.a	\( 2 \cdot 3^{2} \cdot 5^{2} \)	\( 2 \cdot 3^{6} \cdot 5^{2} \)	$0$	$2$	$\Z/2\Z\oplus\Z/12\Z$	\(\Q \times \Q\)	\(\Q \times \Q\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$				$C_2^2$	$C_2^2$	$4$	$0$	2.180.7, 3.720.4	✓	✓	$1$	\( 2 \cdot 3 \)	\(1.000000\)	\(18.778996\)	\(0.195615\)	$[23444,212089,1627179821,4665600]$	$[5861,1422468,457836300,164990835819,36450]$	$[6916057684302385301/36450,5303516319500302/675,1294426477922/3]$	$y^2 + (x^3 + 1)y = x^5 - 4x^4 - 9x^3 + 28x^2 - 6x - 16$