Atkin-Lehner |
2- 3+ 5- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
66240dz |
Isogeny class |
Conductor |
66240 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
331776 |
Modular degree for the optimal curve |
Δ |
27557332254720 = 224 · 33 · 5 · 233 |
Discriminant |
Eigenvalues |
2- 3+ 5- 4 0 4 0 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-243852,-46348016] |
[a1,a2,a3,a4,a6] |
Generators |
[-18216793985070:-174294820189:64096048008] |
Generators of the group modulo torsion |
j |
226568219476347/3893440 |
j-invariant |
L |
8.7038879006402 |
L(r)(E,1)/r! |
Ω |
0.21484162173568 |
Real period |
R |
20.256521595991 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998014 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
66240y1 16560z1 66240ds3 |
Quadratic twists by: -4 8 -3 |