Atkin-Lehner |
7+ 37- 47- |
Signs for the Atkin-Lehner involutions |
Class |
12173c |
Isogeny class |
Conductor |
12173 |
Conductor |
∏ cp |
42 |
Product of Tamagawa factors cp |
deg |
682752 |
Modular degree for the optimal curve |
Δ |
-6.161441619087E+19 |
Discriminant |
Eigenvalues |
0 -1 -1 7+ -2 -1 -6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-88166821,318673718128] |
[a1,a2,a3,a4,a6] |
Generators |
[6218:4004913:8] |
Generators of the group modulo torsion |
j |
-75794774056299878301275521024/61614416190870425939 |
j-invariant |
L |
1.8596219647949 |
L(r)(E,1)/r! |
Ω |
0.16412354754756 |
Real period |
R |
0.26977672679581 |
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 |
109557k1 85211j1 |
Quadratic twists by: -3 -7 |