Atkin-Lehner |
2- 3+ 5+ 11- 23- |
Signs for the Atkin-Lehner involutions |
Class |
60720bp |
Isogeny class |
Conductor |
60720 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
152064 |
Modular degree for the optimal curve |
Δ |
-5507259310080 = -1 · 213 · 312 · 5 · 11 · 23 |
Discriminant |
Eigenvalues |
2- 3+ 5+ -5 11- -4 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-5336,-186000] |
[a1,a2,a3,a4,a6] |
Generators |
[100:520:1] [146:-1458:1] |
Generators of the group modulo torsion |
j |
-4102915888729/1344545730 |
j-invariant |
L |
6.9652663840718 |
L(r)(E,1)/r! |
Ω |
0.27471644604006 |
Real period |
R |
3.1692980546284 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999976 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7590j1 |
Quadratic twists by: -4 |