Genus 2 curves of conductor 830

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
830.a.6640.1	830.a	\( 2 \cdot 5 \cdot 83 \)	\( - 2^{4} \cdot 5 \cdot 83 \)	$0$	$1$	$\Z/16\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$1$	2.60.1	✓	✓	$1$	\( 2^{2} \)	\(1.000000\)	\(23.474917\)	\(0.366796\)	$[652,4273,1339719,849920]$	$[163,929,-521,-236991,6640]$	$[115063617043/6640,4023263963/6640,-13842449/6640]$	$y^2 + (x^3 + 1)y = -x^5 + x^4 - 2x^2 + x + 1$
830.a.830000.1	830.a	\( 2 \cdot 5 \cdot 83 \)	\( - 2^{4} \cdot 5^{4} \cdot 83 \)	$0$	$2$	$\Z/2\Z\oplus\Z/8\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2$	✓	✓	$C_2$	$C_2$	$5$	$3$	2.120.3	✓	✓	$1$	\( 2^{4} \)	\(1.000000\)	\(5.868729\)	\(0.366796\)	$[15236,-229487,-1147645831,-106240000]$	$[3809,614082,133745600,33085071919,-830000]$	$[-801779343712318049/830000,-16967946642572289/415000,-4851113741084/2075]$	$y^2 + (x^2 + x)y = x^5 - 2x^4 + 16x^3 + 8x^2 + x$