Atkin-Lehner |
2+ 5+ 17- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
21080d |
Isogeny class |
Conductor |
21080 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
3648 |
Modular degree for the optimal curve |
Δ |
-60921200 = -1 · 24 · 52 · 173 · 31 |
Discriminant |
Eigenvalues |
2+ -1 5+ -2 -3 -2 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,84,205] |
[a1,a2,a3,a4,a6] |
Generators |
[18:-85:1] [34:203:1] |
Generators of the group modulo torsion |
j |
4048192256/3807575 |
j-invariant |
L |
5.6727782438278 |
L(r)(E,1)/r! |
Ω |
1.2918927306497 |
Real period |
R |
0.36592165053924 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42160f1 105400m1 |
Quadratic twists by: -4 5 |