Atkin-Lehner |
3- 11- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
8349b |
Isogeny class |
Conductor |
8349 |
Conductor |
∏ cp |
20 |
Product of Tamagawa factors cp |
deg |
195360 |
Modular degree for the optimal curve |
Δ |
-810205283204893521 = -1 · 310 · 1110 · 232 |
Discriminant |
Eigenvalues |
1 3- 1 0 11- -1 1 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-6918178,-7004541535] |
[a1,a2,a3,a4,a6] |
Generators |
[26785:4348304:1] |
Generators of the group modulo torsion |
j |
-1411796061716161/31236921 |
j-invariant |
L |
6.4466575967876 |
L(r)(E,1)/r! |
Ω |
0.046544788051238 |
Real period |
R |
6.9252196289849 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25047h1 8349e1 |
Quadratic twists by: -3 -11 |