Genus 2 curves of conductor 100325

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
100325.a.100325.1	100325.a	\( 5^{2} \cdot 4013 \)	\( 5^{2} \cdot 4013 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.396628\)	\(7.575309\)	\(3.004578\)	$[416,4420,595015,401300]$	$[208,1066,-2719,-425477,100325]$	$[389328928768/100325,9592840192/100325,-117634816/100325]$	$y^2 + x^2y = x^5 - 2x^4 + 4x^3 - 4x^2 + 3x - 1$
100325.b.100325.1	100325.b	\( 5^{2} \cdot 4013 \)	\( 5^{2} \cdot 4013 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.093538\)	\(13.292801\)	\(1.243385\)	$[3060,-200871,-238360131,12841600]$	$[765,32754,2568348,222990426,100325]$	$[10480141999125/4013,586554865290/4013,60122458332/4013]$	$y^2 + (x^2 + x + 1)y = -x^5 + 3x^4 - 10x^2 + 2x + 8$