Atkin-Lehner |
7- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
47971l |
Isogeny class |
Conductor |
47971 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
253440 |
Modular degree for the optimal curve |
Δ |
-62081141969 = -1 · 78 · 112 · 89 |
Discriminant |
Eigenvalues |
-1 -1 3 7- 11- -4 -7 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-464374,121607268] |
[a1,a2,a3,a4,a6] |
Generators |
[398:-371:1] [48:9947:1] |
Generators of the group modulo torsion |
j |
-94132418755192273/527681 |
j-invariant |
L |
5.9733445183654 |
L(r)(E,1)/r! |
Ω |
0.75409092841023 |
Real period |
R |
0.99015654036568 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999981 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
6853d1 |
Quadratic twists by: -7 |