Atkin-Lehner |
2- 11+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
21824u |
Isogeny class |
Conductor |
21824 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
5632 |
Modular degree for the optimal curve |
Δ |
-3841024 = -1 · 210 · 112 · 31 |
Discriminant |
Eigenvalues |
2- -2 3 1 11+ 4 -2 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-129,-617] |
[a1,a2,a3,a4,a6] |
Generators |
[138:407:8] |
Generators of the group modulo torsion |
j |
-233644288/3751 |
j-invariant |
L |
4.7697516398509 |
L(r)(E,1)/r! |
Ω |
0.70717645174413 |
Real period |
R |
3.372391450597 |
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 |
21824g1 5456c1 |
Quadratic twists by: -4 8 |