Genus 2 curves of conductor 1270

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
1270.a.1270.1	1270.a	\( 2 \cdot 5 \cdot 127 \)	\( 2 \cdot 5 \cdot 127 \)	$0$	$1$	$\Z/6\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$2$	$0$	2.15.1, 3.80.1	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(17.051434\)	\(0.473651\)	$[2612,-8063,-7006415,162560]$	$[653,18103,680921,29230701,1270]$	$[118731486838493/1270,5040691228931/1270,290350842689/1270]$	$y^2 + (x^3 + 1)y = -2x^4 + 5x^2 - 2x - 3$
1270.a.325120.1	1270.a	\( 2 \cdot 5 \cdot 127 \)	\( 2^{9} \cdot 5 \cdot 127 \)	$0$	$1$	$\Z/2\Z$	\(\Q\)	\(\Q\)		$\mathrm{USp}(4)$	$2,3$	✓	✓	$C_2$	$C_2$	$1$	$1$	2.60.1, 3.80.2	✓	✓	$1$	\( 1 \)	\(1.000000\)	\(1.894604\)	\(0.473651\)	$[239204,126763297,10436094933809,41615360]$	$[59801,143724846,437833820176,1381517230655315,325120]$	$[764790054928595680699001/325120,15368348330455841308623/162560,97860226229056869361/20320]$	$y^2 + (x^2 + x)y = x^5 + 17x^4 + 76x^3 + 14x^2 - 32x + 3$