Genus 2 curves of conductor 5329

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
5329.a.5329.1	5329.a	\( 73^{2} \)	\( 73^{2} \)	$0$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$0$	$0$	2.12.2, 3.2160.23	✓	✓	$4$	\( 1 \)	\(1.000000\)	\(0.296753\)	\(1.187013\)	$[139452,310895097,16328330150691,-682112]$	$[34863,37688903,-3247242817,-383415508918120,-5329]$	$[-51501962646275676450543/5329,-1597010473992743939241/5329,3946792339710402273/5329]$	$y^2 + (x^3 + x + 1)y = -x^6 - 8x^5 - 16x^4 + 25x^3 - 40x^2 + 31x - 8$
5329.b.5329.1	5329.b	\( 73^{2} \)	\( 73^{2} \)	$2$	$2$	$\mathsf{trivial}$	\(\mathsf{RM}\)	\(\mathsf{RM}\)	✓	$\mathrm{SU}(2)\times\mathrm{SU}(2)$		✓	✓	$C_2$	$C_2$	$10$	$0$	2.12.2, 3.2160.18	✓	✓	$1$	\( 1 \)	\(0.010713\)	\(24.093314\)	\(0.258121\)	$[188,3721,413963,-682112]$	$[47,-63,-3485,-41941,-5329]$	$[-229345007/5329,6540849/5329,7698365/5329]$	$y^2 + (x^3 + x^2 + 1)y = x^3 - x$