Atkin-Lehner |
2+ 3+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
60984b |
Isogeny class |
Conductor |
60984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
591360 |
Modular degree for the optimal curve |
Δ |
-17120171596019184 = -1 · 24 · 33 · 75 · 119 |
Discriminant |
Eigenvalues |
2+ 3+ 3 7+ 11+ 7 2 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,51909,-4348377] |
[a1,a2,a3,a4,a6] |
Generators |
[11495:137093:125] |
Generators of the group modulo torsion |
j |
15185664/16807 |
j-invariant |
L |
8.2309661085612 |
L(r)(E,1)/r! |
Ω |
0.21038700821948 |
Real period |
R |
4.8903721397401 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000101 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
121968m1 60984bk1 60984br1 |
Quadratic twists by: -4 -3 -11 |