Genus 2 curves of conductor 1575

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
1575.a.23625.1	1575.a	\( 3^{2} \cdot 5^{2} \cdot 7 \)	\( 3^{3} \cdot 5^{3} \cdot 7 \)	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$8$	$2$	2.180.3	✓	✓	$1$	\( 2^{2} \)	\(0.054364\)	\(17.779771\)	\(0.241646\)	$[5748,48105,93031605,3024000]$	$[1437,84036,6376864,525376068,23625]$	$[226944716565591/875,9235744556604/875,1463114053024/2625]$	$y^2 + (x^3 + 1)y = x^5 - x^4 - 6x^3 + 2x^2 + 7x - 4$
1575.a.165375.1	1575.a	\( 3^{2} \cdot 5^{2} \cdot 7 \)	\( - 3^{3} \cdot 5^{3} \cdot 7^{2} \)	$1$	$3$	$\Z/2\Z\oplus\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$10$	$2$	2.180.3	✓	✓	$1$	\( 2^{3} \)	\(0.027182\)	\(17.779771\)	\(0.241646\)	$[12,19305,2541195,21168000]$	$[3,-804,-34624,-187572,165375]$	$[9/6125,-804/6125,-34624/18375]$	$y^2 + (x^2 + x + 1)y = -x^5 + 2x^4 + x^2 - 2x$