Atkin-Lehner |
3+ 7- 13- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
55419b |
Isogeny class |
Conductor |
55419 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
73728 |
Modular degree for the optimal curve |
Δ |
-762838821927 = -1 · 33 · 78 · 132 · 29 |
Discriminant |
Eigenvalues |
-1 3+ 2 7- -4 13- 6 6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-687,-42876] |
[a1,a2,a3,a4,a6] |
Generators |
[66:419:1] |
Generators of the group modulo torsion |
j |
-304821217/6484023 |
j-invariant |
L |
3.5003570926867 |
L(r)(E,1)/r! |
Ω |
0.38786474524728 |
Real period |
R |
4.5123424278726 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000503 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
7917c1 |
Quadratic twists by: -7 |