Atkin-Lehner |
3+ 5+ 7- 83- |
Signs for the Atkin-Lehner involutions |
Class |
8715d |
Isogeny class |
Conductor |
8715 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
Δ |
4005077710424450625 = 318 · 54 · 74 · 832 |
Discriminant |
Eigenvalues |
1 3+ 5+ 7- 4 -2 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-8037368,8766513147] |
[a1,a2,a3,a4,a6] |
Generators |
[408714:3764041:216] |
Generators of the group modulo torsion |
j |
57420286739327390326341769/4005077710424450625 |
j-invariant |
L |
4.1506941505661 |
L(r)(E,1)/r! |
Ω |
0.23515556638554 |
Real period |
R |
8.8254218566125 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
26145p2 43575m2 61005w2 |
Quadratic twists by: -3 5 -7 |