Atkin-Lehner |
2+ 5- 7- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
117040w |
Isogeny class |
Conductor |
117040 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
884736 |
Modular degree for the optimal curve |
Δ |
-24410373352750000 = -1 · 24 · 56 · 76 · 112 · 193 |
Discriminant |
Eigenvalues |
2+ 0 5- 7- 11- 0 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-154922,24644639] |
[a1,a2,a3,a4,a6] |
Generators |
[523:9310:1] |
Generators of the group modulo torsion |
j |
-25700585323982616576/1525648334546875 |
j-invariant |
L |
7.7848807384539 |
L(r)(E,1)/r! |
Ω |
0.37307080413689 |
Real period |
R |
0.38642653472769 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000004774 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
58520e1 |
Quadratic twists by: -4 |