Atkin-Lehner |
5+ 7+ 17+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
129115a |
Isogeny class |
Conductor |
129115 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
16219392 |
Modular degree for the optimal curve |
Δ |
-3.019180717675E+24 |
Discriminant |
Eigenvalues |
-1 1 5+ 7+ 0 -4 17+ 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-26999981,-99525303130] |
[a1,a2,a3,a4,a6] |
Generators |
[779943:129729847:27] |
Generators of the group modulo torsion |
j |
-377598072442170810769/523726789125078125 |
j-invariant |
L |
3.1272268858514 |
L(r)(E,1)/r! |
Ω |
0.031518027270431 |
Real period |
R |
8.2683549303881 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000165388 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
129115y1 |
Quadratic twists by: -7 |