Genus 2 curve search results

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
206027.a.206027.1	206027.a	\( 206027 \)	\( -206027 \)	$0$	$1$	$\Z/5\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$5$	✓	✓	$C_2$	$C_2$	$0$	$0$				$18$	\( 1 \)	\(1.000000\)	\(3.861920\)	\(2.780582\)	$[146200,280996,13643019408,824108]$	$[73100,222603584,903643153288,4125989723926936,206027]$	$[2087309668526510000000000/206027,86952942511121344000000/206027,4828716590341289680000/206027]$	$y^2 + y = -3x^6 - x^5 - 20x^4 - 5x^3 - 44x^2 - 6x - 32$
516443.b.516443.1	516443.b	\( 17^{2} \cdot 1787 \)	\( - 17^{2} \cdot 1787 \)	$0$	$1$	$\mathsf{trivial}$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$		✓	✓	$C_2$	$C_2$	$0$	$0$				$18$	\( 1 \)	\(1.000000\)	\(0.531606\)	\(9.568905\)	$[3460,30814345,-18826218827,-66104704]$	$[865,-1252755,571473541,-268767619265,-516443]$	$[-484262162790625/516443,810801357541875/516443,-427590790214725/516443]$	$y^2 + (x^3 + x + 1)y = -11x^6 - 9x^5 + 39x^4 - 47x^2 + 32x - 7$