Atkin-Lehner |
2- 3+ 11+ 13- |
Signs for the Atkin-Lehner involutions |
Class |
6864o |
Isogeny class |
Conductor |
6864 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
74880 |
Modular degree for the optimal curve |
Δ |
-423251813597184 = -1 · 225 · 36 · 113 · 13 |
Discriminant |
Eigenvalues |
2- 3+ 3 1 11+ 13- 0 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1663784,-825471888] |
[a1,a2,a3,a4,a6] |
Generators |
[8761115117:323917865244:3869893] |
Generators of the group modulo torsion |
j |
-124352595912593543977/103332962304 |
j-invariant |
L |
4.379721259329 |
L(r)(E,1)/r! |
Ω |
0.066465347502459 |
Real period |
R |
16.473701800652 |
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 |
858d1 27456ch1 20592bw1 75504bp1 |
Quadratic twists by: -4 8 -3 -11 |