Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312cv |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-10676346842824704 = -1 · 214 · 36 · 197 |
Discriminant |
Eigenvalues |
2- 3+ 3 3 -1 -2 -5 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-82789,10457341] |
[a1,a2,a3,a4,a6] |
Generators |
[-37420:360639:125] |
Generators of the group modulo torsion |
j |
-81415168/13851 |
j-invariant |
L |
7.5189495730353 |
L(r)(E,1)/r! |
Ω |
0.39028045970548 |
Real period |
R |
4.8163758815489 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000498 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
69312bw1 17328o1 3648bj1 |
Quadratic twists by: -4 8 -19 |