Atkin-Lehner |
2+ 3+ 19- 89- |
Signs for the Atkin-Lehner involutions |
Class |
40584d |
Isogeny class |
Conductor |
40584 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
11904 |
Modular degree for the optimal curve |
Δ |
-87904944 = -1 · 24 · 32 · 193 · 89 |
Discriminant |
Eigenvalues |
2+ 3+ 3 0 -1 -1 3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-299,-1944] |
[a1,a2,a3,a4,a6] |
Generators |
[35:171:1] |
Generators of the group modulo torsion |
j |
-185382602752/5494059 |
j-invariant |
L |
6.4710721977468 |
L(r)(E,1)/r! |
Ω |
0.57289182752309 |
Real period |
R |
0.94128767521453 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000005 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81168y1 121752bh1 |
Quadratic twists by: -4 -3 |