Atkin-Lehner |
2- 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208bn |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
995328 |
Modular degree for the optimal curve |
Δ |
-710261334237708288 = -1 · 216 · 33 · 712 · 29 |
Discriminant |
Eigenvalues |
2- 3+ -4 7- 0 -2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-345760,88251136] |
[a1,a2,a3,a4,a6] |
Generators |
[-240:12544:1] |
Generators of the group modulo torsion |
j |
-9486391169809/1473906672 |
j-invariant |
L |
2.906285528536 |
L(r)(E,1)/r! |
Ω |
0.27574553163283 |
Real period |
R |
2.6349343832207 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999974563 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
8526z1 9744s1 |
Quadratic twists by: -4 -7 |