Atkin-Lehner |
2+ 3- 13+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69966s |
Isogeny class |
Conductor |
69966 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
698880 |
Modular degree for the optimal curve |
Δ |
-4626135369962496 = -1 · 210 · 319 · 132 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -3 4 0 13+ -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,1314,-3272684] |
[a1,a2,a3,a4,a6] |
Generators |
[1196:40730:1] |
Generators of the group modulo torsion |
j |
2035680647/37549495296 |
j-invariant |
L |
3.4740316700517 |
L(r)(E,1)/r! |
Ω |
0.20053923757654 |
Real period |
R |
4.330862769326 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999965877 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23322n1 69966bi1 |
Quadratic twists by: -3 13 |