Atkin-Lehner |
2- 3- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
51984bw |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
276480 |
Modular degree for the optimal curve |
Δ |
-24207398469107712 = -1 · 220 · 311 · 194 |
Discriminant |
Eigenvalues |
2- 3- 0 -1 -2 -3 -4 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-157035,25094554] |
[a1,a2,a3,a4,a6] |
Generators |
[245:1152:1] |
Generators of the group modulo torsion |
j |
-1100553625/62208 |
j-invariant |
L |
4.8396020443505 |
L(r)(E,1)/r! |
Ω |
0.37365746929226 |
Real period |
R |
1.6189968226552 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.9999999999971 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6498r1 17328z1 51984cj1 |
Quadratic twists by: -4 -3 -19 |