Genus 2 curves of conductor 6827

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
6827.a.6827.1	6827.a	\( 6827 \)	\( -6827 \)	$0$	$0$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$3$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(12.595822\)	\(0.503833\)	$[1280,-3500,-1012409,-27308]$	$[640,17650,615601,20615535,-6827]$	$[-107374182400000/6827,-4626841600000/6827,-252150169600/6827]$	$y^2 + x^2y = x^5 + x^4 - 6x^2 + 5x - 1$
6827.a.6827.2	6827.a	\( 6827 \)	\( -6827 \)	$0$	$0$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,5$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.6.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(0.503833\)	\(0.503833\)	$[487400,150770140,23877835098591,-27308]$	$[243700,2449442060,32550891274601,483221449580805025,-6827]$	$[-859562867320759570000000000/6827,-35451430045007273180000000/6827,-1933187342022258263690000/6827]$	$y^2 + x^2y = x^5 + 21x^4 + 95x^3 - 191x^2 + 69x - 7$