Atkin-Lehner |
3+ 11- 47- |
Signs for the Atkin-Lehner involutions |
Class |
51183b |
Isogeny class |
Conductor |
51183 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
129600 |
Modular degree for the optimal curve |
Δ |
1638872852661 = 39 · 116 · 47 |
Discriminant |
Eigenvalues |
-2 3+ 3 -1 11- 0 0 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-9801,368354] |
[a1,a2,a3,a4,a6] |
Generators |
[42:175:1] |
Generators of the group modulo torsion |
j |
2985984/47 |
j-invariant |
L |
3.9520882459352 |
L(r)(E,1)/r! |
Ω |
0.84445969237957 |
Real period |
R |
2.3400099978288 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000182 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51183a1 423d1 |
Quadratic twists by: -3 -11 |