Atkin-Lehner |
2+ 3+ 5+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
21150d |
Isogeny class |
Conductor |
21150 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
253440 |
Modular degree for the optimal curve |
Δ |
-303137095680000000 = -1 · 222 · 39 · 57 · 47 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -3 -2 1 7 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-66192,27305216] |
[a1,a2,a3,a4,a6] |
Generators |
[928:27184:1] |
Generators of the group modulo torsion |
j |
-104287581243/985661440 |
j-invariant |
L |
3.2378163483477 |
L(r)(E,1)/r! |
Ω |
0.26194443112277 |
Real period |
R |
1.5450874134208 |
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 |
21150bt1 4230u1 |
Quadratic twists by: -3 5 |