Genus 2 curves of conductor 100315

Results (unique match)

 

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
100315.a.501575.1	100315.a	\( 5 \cdot 20063 \)	\( - 5^{2} \cdot 20063 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$6$	$0$		✓	✓	$1$	\( 2 \)	\(0.052093\)	\(14.989420\)	\(1.561682\)	$[4380,252849,473905527,64201600]$	$[1095,39424,-338316,-481176949,501575]$	$[62969549637375/20063,2070441838080/20063,-16225973676/20063]$	$y^2 + (x^3 + x + 1)y = 2x^5 + 3x^4 + x^3 + 2x^2 - 5x + 1$