Atkin-Lehner |
2- 3- 5- 17- 73- |
Signs for the Atkin-Lehner involutions |
Class |
111690cd |
Isogeny class |
Conductor |
111690 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
677376 |
Modular degree for the optimal curve |
Δ |
-2249326668447360 = -1 · 27 · 312 · 5 · 17 · 733 |
Discriminant |
Eigenvalues |
2- 3- 5- -1 -3 -4 17- -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,31738,677909] |
[a1,a2,a3,a4,a6] |
Generators |
[129:-2693:1] [99:2137:1] |
Generators of the group modulo torsion |
j |
4850066347489511/3085496115840 |
j-invariant |
L |
17.416506865031 |
L(r)(E,1)/r! |
Ω |
0.2871568081992 |
Real period |
R |
0.72204231809034 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999996756 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
37230k1 |
Quadratic twists by: -3 |