Atkin-Lehner |
2- 3+ 11- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
67518bc |
Isogeny class |
Conductor |
67518 |
Conductor |
∏ cp |
128 |
Product of Tamagawa factors cp |
deg |
921600 |
Modular degree for the optimal curve |
Δ |
15662507197024512 = 28 · 33 · 119 · 312 |
Discriminant |
Eigenvalues |
2- 3+ -4 0 11- 4 6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-70082,-3821375] |
[a1,a2,a3,a4,a6] |
Generators |
[355:3815:1] |
Generators of the group modulo torsion |
j |
795824837163/327447296 |
j-invariant |
L |
8.218162186268 |
L(r)(E,1)/r! |
Ω |
0.30423659963071 |
Real period |
R |
0.84413765021155 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
67518b1 6138b1 |
Quadratic twists by: -3 -11 |