Atkin-Lehner |
7- 61- |
Signs for the Atkin-Lehner involutions |
Class |
2989c |
Isogeny class |
Conductor |
2989 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1728 |
Modular degree for the optimal curve |
Δ |
2461570027 = 79 · 61 |
Discriminant |
Eigenvalues |
-1 -1 0 7- -5 -4 5 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-1373,18864] |
[a1,a2,a3,a4,a6] |
Generators |
[-8:175:1] |
Generators of the group modulo torsion |
j |
2433138625/20923 |
j-invariant |
L |
1.5758646128072 |
L(r)(E,1)/r! |
Ω |
1.4558874329938 |
Real period |
R |
0.27060207010075 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
47824r1 26901t1 74725m1 427c1 |
Quadratic twists by: -4 -3 5 -7 |