Atkin-Lehner |
3+ 11- 59- |
Signs for the Atkin-Lehner involutions |
Class |
21417g |
Isogeny class |
Conductor |
21417 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
489600 |
Modular degree for the optimal curve |
Δ |
-148478009921583507 = -1 · 317 · 117 · 59 |
Discriminant |
Eigenvalues |
2 3+ 2 4 11- -7 3 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,131608,2404049] |
[a1,a2,a3,a4,a6] |
Generators |
[169735954:18650985431:8242408] |
Generators of the group modulo torsion |
j |
142302054182912/83811965787 |
j-invariant |
L |
10.733387321713 |
L(r)(E,1)/r! |
Ω |
0.19784871750227 |
Real period |
R |
13.562619279539 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64251v1 1947b1 |
Quadratic twists by: -3 -11 |