Genus 2 curves of conductor 164326

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
164326.a.328652.1	164326.a	\( 2 \cdot 82163 \)	\( - 2^{2} \cdot 82163 \)	$3$	$3$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$15$	$1$	2.6.1	✓	✓	$1$	\( 2 \)	\(0.033199\)	\(16.734081\)	\(1.111093\)	$[500,21049,1530861,-42067456]$	$[125,-226,13712,415731,-328652]$	$[-30517578125/328652,220703125/164326,-53562500/82163]$	$y^2 + (x^3 + 1)y = 2x^4 + x^3 - 2x^2 - x$
164326.b.328652.1	164326.b	\( 2 \cdot 82163 \)	\( 2^{2} \cdot 82163 \)	$1$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$4$	$0$		✓	✓	$1$	\( 2 \)	\(0.049033\)	\(14.279664\)	\(1.400355\)	$[4684,282841,690551139,-42067456]$	$[1171,45350,-2040624,-1111548301,-328652]$	$[-2201833501574851/328652,-36409773809425/164326,699546823596/82163]$	$y^2 + (x^3 + 1)y = 2x^5 + 4x^4 + 5x^3 + 8x^2 - 3x$