Atkin-Lehner |
2+ 3+ 23- 29- |
Signs for the Atkin-Lehner involutions |
Class |
64032i |
Isogeny class |
Conductor |
64032 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
423936 |
Modular degree for the optimal curve |
Δ |
-1221059521032192 = -1 · 212 · 312 · 23 · 293 |
Discriminant |
Eigenvalues |
2+ 3+ 0 2 4 -1 -3 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-680893,-216034859] |
[a1,a2,a3,a4,a6] |
Generators |
[26229:167156:27] |
Generators of the group modulo torsion |
j |
-8523167239536832000/298110234627 |
j-invariant |
L |
6.1728852279681 |
L(r)(E,1)/r! |
Ω |
0.083099589249915 |
Real period |
R |
6.1902484351384 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000306 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64032bb1 128064bi1 |
Quadratic twists by: -4 8 |