Genus 2 curves in isogeny class 10125.a of discriminant 10125

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
10125.a.10125.1	10125.a	\( 3^{4} \cdot 5^{3} \)	\( 3^{4} \cdot 5^{3} \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$5$	✓	✓	$C_2$	$C_2$	$2$	$0$		✓	✓	$1$	\( 1 \)	\(0.094033\)	\(11.744269\)	\(1.104351\)	$[420,6705,902025,1296000]$	$[105,180,-1700,-52725,10125]$	$[1260525,20580,-16660/9]$	$y^2 + (x^3 + x + 1)y = -x^2 + x - 1$
10125.a.10125.2	10125.a	\( 3^{4} \cdot 5^{3} \)	\( 3^{4} \cdot 5^{3} \)	$1$	$1$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$5$	✓	✓	$C_2$	$C_2$	$2$	$0$		✓	✓	$1$	\( 1 \)	\(2.350830\)	\(11.744269\)	\(1.104351\)	$[27780,151768305,775034217225,1296000]$	$[6945,-4313970,2210480200,-814638042975,10125]$	$[1595755016890725,-142724601457530,94771685998760/9]$	$y^2 + (x^3 + x^2 + 1)y = 9x^4 + 28x^3 - x^2 - 34x + 13$