Atkin-Lehner |
11- 17- 47- |
Signs for the Atkin-Lehner involutions |
Class |
8789c |
Isogeny class |
Conductor |
8789 |
Conductor |
∏ cp |
63 |
Product of Tamagawa factors cp |
deg |
82656 |
Modular degree for the optimal curve |
Δ |
56704050014395949 = 113 · 177 · 473 |
Discriminant |
Eigenvalues |
-1 0 1 -5 11- -5 17- 5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-148462,-18764872] |
[a1,a2,a3,a4,a6] |
Generators |
[-253:1724:1] [512:6008:1] |
Generators of the group modulo torsion |
j |
361881923610251311281/56704050014395949 |
j-invariant |
L |
3.6283625345476 |
L(r)(E,1)/r! |
Ω |
0.24578628921269 |
Real period |
R |
0.23432167957149 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999944 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
79101c1 96679b1 |
Quadratic twists by: -3 -11 |