Atkin-Lehner |
3- 23- 41+ |
Signs for the Atkin-Lehner involutions |
Class |
115989m |
Isogeny class |
Conductor |
115989 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
1935360 |
Modular degree for the optimal curve |
Δ |
490502076814196289 = 32 · 234 · 417 |
Discriminant |
Eigenvalues |
-1 3- -2 4 0 2 -6 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-309339,-57033576] |
[a1,a2,a3,a4,a6] |
Generators |
[-1305580143:-8560340939:5545233] |
Generators of the group modulo torsion |
j |
689167345537/103261329 |
j-invariant |
L |
5.735195419265 |
L(r)(E,1)/r! |
Ω |
0.20446987672227 |
Real period |
R |
14.024548424528 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000007736 |
(Analytic) order of Ш |
t |
4 |
Number of elements in the torsion subgroup |
Twists |
2829e1 |
Quadratic twists by: 41 |