Atkin-Lehner |
2+ 23- 29- |
Signs for the Atkin-Lehner involutions |
Class |
42688i |
Isogeny class |
Conductor |
42688 |
Conductor |
∏ cp |
18 |
Product of Tamagawa factors cp |
deg |
716544 |
Modular degree for the optimal curve |
Δ |
-491153934159020864 = -1 · 26 · 232 · 299 |
Discriminant |
Eigenvalues |
2+ 1 3 -4 5 -5 6 -8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-17524,33724378] |
[a1,a2,a3,a4,a6] |
Generators |
[-8493:77372:27] |
Generators of the group modulo torsion |
j |
-9299685341217088/7674280221234701 |
j-invariant |
L |
7.4370487493003 |
L(r)(E,1)/r! |
Ω |
0.23806106121227 |
Real period |
R |
1.7355605022397 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999962 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
42688d1 21344c1 |
Quadratic twists by: -4 8 |