Atkin-Lehner |
2- 3+ 103+ |
Signs for the Atkin-Lehner involutions |
Class |
59328z |
Isogeny class |
Conductor |
59328 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
129024 |
Modular degree for the optimal curve |
Δ |
-11944304050176 = -1 · 232 · 33 · 103 |
Discriminant |
Eigenvalues |
2- 3+ 1 0 -6 -1 -8 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-8172,-329392] |
[a1,a2,a3,a4,a6] |
Generators |
[538:12288:1] [304:5028:1] |
Generators of the group modulo torsion |
j |
-8527173507/1687552 |
j-invariant |
L |
10.216287655888 |
L(r)(E,1)/r! |
Ω |
0.2484144299124 |
Real period |
R |
5.1407478922919 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999911 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
59328a1 14832e1 59328ba1 |
Quadratic twists by: -4 8 -3 |