Atkin-Lehner |
2- 3+ 19+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
81168bu |
Isogeny class |
Conductor |
81168 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
79872 |
Modular degree for the optimal curve |
Δ |
-15958278144 = -1 · 220 · 32 · 19 · 89 |
Discriminant |
Eigenvalues |
2- 3+ 3 2 -5 1 7 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1464,22896] |
[a1,a2,a3,a4,a6] |
Generators |
[60:384:1] |
Generators of the group modulo torsion |
j |
-84778086457/3896064 |
j-invariant |
L |
7.7004186044086 |
L(r)(E,1)/r! |
Ω |
1.2276064564751 |
Real period |
R |
0.78408867941907 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002568 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10146h1 |
Quadratic twists by: -4 |