Genus 2 curves of conductor 126859

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
126859.a.126859.1	126859.a	\( 126859 \)	\( -126859 \)	$2$	$2$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$7$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(0.250173\)	\(8.705737\)	\(2.177941\)	$[1984,5584,5854832,-507436]$	$[992,40072,1865616,61231472,-126859]$	$[-960634900447232/126859,-39117945307136/126859,-1835885543424/126859]$	$y^2 + y = x^5 - 3x^4 + 7x^2 + 4x$
126859.b.126859.1	126859.b	\( 126859 \)	\( -126859 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.302295\)	\(3.803714\)	\(4.953558\)	$[18528,46416,283353360,-507436]$	$[9264,3568168,1828822192,1052596477616,-126859]$	$[-68232727503987277824/126859,-2836879788910804992/126859,-156952622199877632/126859]$	$y^2 + y = x^5 - 8x^4 - 38x^3 - 29x^2 - 8x - 1$