Atkin-Lehner |
2- 3+ 5- 11- 19- |
Signs for the Atkin-Lehner involutions |
Class |
68970bz |
Isogeny class |
Conductor |
68970 |
Conductor |
∏ cp |
64 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
421745008626562500 = 22 · 36 · 58 · 117 · 19 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 11- 2 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-333660,-67420935] |
[a1,a2,a3,a4,a6] |
Generators |
[-407:1283:1] |
Generators of the group modulo torsion |
j |
2318889846161881/238064062500 |
j-invariant |
L |
8.4520292866312 |
L(r)(E,1)/r! |
Ω |
0.19995936831355 |
Real period |
R |
2.641795855181 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999827 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6270d1 |
Quadratic twists by: -11 |