Atkin-Lehner |
2+ 3- 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304do |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
61440 |
Modular degree for the optimal curve |
Δ |
-6166689984 = -1 · 26 · 32 · 77 · 13 |
Discriminant |
Eigenvalues |
2+ 3- 3 7- 0 13+ 0 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-359,4479] |
[a1,a2,a3,a4,a6] |
Generators |
[30:147:1] |
Generators of the group modulo torsion |
j |
-681472/819 |
j-invariant |
L |
11.636707878928 |
L(r)(E,1)/r! |
Ω |
1.2146139121387 |
Real period |
R |
1.1975727132426 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000045124 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304bd1 61152bn1 17472r1 |
Quadratic twists by: -4 8 -7 |