Atkin-Lehner |
2+ 3- 23- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
4002f |
Isogeny class |
Conductor |
4002 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-17186581700352 = -1 · 28 · 38 · 233 · 292 |
Discriminant |
Eigenvalues |
2+ 3- 2 0 2 -6 -8 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-12275,559118] |
[a1,a2,a3,a4,a6] |
Generators |
[-42:1021:1] |
Generators of the group modulo torsion |
j |
-204520739414888233/17186581700352 |
j-invariant |
L |
3.5133929378841 |
L(r)(E,1)/r! |
Ω |
0.67846860424996 |
Real period |
R |
0.215767349432 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
32016m1 128064u1 12006n1 100050bl1 |
Quadratic twists by: -4 8 -3 5 |