Atkin-Lehner |
2- 3+ 11- 47+ |
Signs for the Atkin-Lehner involutions |
Class |
68244a |
Isogeny class |
Conductor |
68244 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
138240 |
Modular degree for the optimal curve |
Δ |
-18992040959232 = -1 · 28 · 34 · 117 · 47 |
Discriminant |
Eigenvalues |
2- 3+ 2 1 11- 1 4 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6332,-283512] |
[a1,a2,a3,a4,a6] |
Generators |
[58618:5017023:8] |
Generators of the group modulo torsion |
j |
-61918288/41877 |
j-invariant |
L |
7.0613896392858 |
L(r)(E,1)/r! |
Ω |
0.25977013425366 |
Real period |
R |
6.7958058953422 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000151 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6204c1 |
Quadratic twists by: -11 |