Atkin-Lehner |
2+ 3- 7+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
108192o |
Isogeny class |
Conductor |
108192 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
172032 |
Modular degree for the optimal curve |
Δ |
-678580224 = -1 · 212 · 3 · 74 · 23 |
Discriminant |
Eigenvalues |
2+ 3- -1 7+ 6 -1 3 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-30641,-2074689] |
[a1,a2,a3,a4,a6] |
Generators |
[1957440747923073:20447170371720996:7586148816449] |
Generators of the group modulo torsion |
j |
-323515119424/69 |
j-invariant |
L |
9.007785651356 |
L(r)(E,1)/r! |
Ω |
0.18042330692808 |
Real period |
R |
24.962921378407 |
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 |
108192y1 108192j1 |
Quadratic twists by: -4 -7 |