Atkin-Lehner |
2+ 3- 23- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
4002g |
Isogeny class |
Conductor |
4002 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
2112 |
Modular degree for the optimal curve |
Δ |
-194769336 = -1 · 23 · 3 · 234 · 29 |
Discriminant |
Eigenvalues |
2+ 3- -3 -3 2 0 3 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-445,3632] |
[a1,a2,a3,a4,a6] |
Generators |
[6:31:1] |
Generators of the group modulo torsion |
j |
-9714044119753/194769336 |
j-invariant |
L |
2.4627220460153 |
L(r)(E,1)/r! |
Ω |
1.7903554578704 |
Real period |
R |
0.34388730394141 |
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 |
32016n1 128064v1 12006o1 100050bm1 |
Quadratic twists by: -4 8 -3 5 |