Atkin-Lehner |
2- 3+ 7- 13+ |
Signs for the Atkin-Lehner involutions |
Class |
122304ex |
Isogeny class |
Conductor |
122304 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
552960 |
Modular degree for the optimal curve |
Δ |
-7211150418640896 = -1 · 221 · 33 · 73 · 135 |
Discriminant |
Eigenvalues |
2- 3+ 1 7- 1 13+ 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,21215,3901633] |
[a1,a2,a3,a4,a6] |
Generators |
[509:12096:1] |
Generators of the group modulo torsion |
j |
11743520417/80199288 |
j-invariant |
L |
7.0063844152224 |
L(r)(E,1)/r! |
Ω |
0.30436712266111 |
Real period |
R |
2.8774397398115 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999733462 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
122304cw1 30576cv1 122304hy1 |
Quadratic twists by: -4 8 -7 |