Genus 2 curve search results

Results (4 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
2187.a.6561.1	2187.a	\( 3^{7} \)	\( 3^{8} \)	$0$	$1$	$\Z/6\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_3)$		✓		$C_2$	$D_6$	$3$	$1$	2.120.1, 3.5760.5	✓	✓	$1$	\( 2 \)	\(1.000000\)	\(10.925677\)	\(0.606982\)	$[124,297,13275,3456]$	$[93,249,-239,-21057,6561]$	$[28629151/27,2472653/81,-229679/729]$	$y^2 + (x^3 + 1)y = -1$
26244.d.314928.1	26244.d	\( 2^{2} \cdot 3^{8} \)	\( 2^{4} \cdot 3^{9} \)	$1$	$1$	$\Z/3\Z\oplus\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_3)$		✓		$C_2$	$D_6$	$6$	$0$	2.20.3, 3.5760.3	✓	✓	$1$	\( 3^{2} \)	\(0.985565\)	\(12.739642\)	\(1.395083\)	$[24,189,1107,-162]$	$[72,-918,-3024,-265113,-314928]$	$[-6144,1088,448/9]$	$y^2 + y = x^6 - 2x^3$
26244.e.472392.1	26244.e	\( 2^{2} \cdot 3^{8} \)	\( - 2^{3} \cdot 3^{10} \)	$0$	$0$	$\Z/3\Z\oplus\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_3)$		✓		$C_2$	$D_6$	$4$	$0$	2.20.3, 3.5760.3	✓	✓	$1$	\( 3^{2} \)	\(1.000000\)	\(12.048083\)	\(1.338676\)	$[356,3969,419553,248832]$	$[267,1482,-2884,-741588,472392]$	$[5584059449/1944,174127343/2916,-5711041/13122]$	$y^2 + (x^3 + 1)y = 2$
59049.a.177147.1	59049.a	\( 3^{10} \)	\( 3^{11} \)	$1$	$1$	$\Z/3\Z$	\(\mathrm{M}_2(\Q)\)	\(\Q\)		$J(E_3)$		✓		$C_2$	$D_6$	$4$	$0$	2.20.3, 3.5760.8	✓	✓	$1$	\( 3 \)	\(0.712785\)	\(8.055321\)	\(1.913904\)	$[52,-63,-111,384]$	$[117,783,-2079,-214083,177147]$	$[371293/3,63713/9,-13013/81]$	$y^2 + (x^3 + 1)y = x^3 - 1$