Atkin-Lehner |
2- 23- 59- |
Signs for the Atkin-Lehner involutions |
Class |
21712j |
Isogeny class |
Conductor |
21712 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
7168 |
Modular degree for the optimal curve |
Δ |
-127840256 = -1 · 212 · 232 · 59 |
Discriminant |
Eigenvalues |
2- -1 -3 -1 0 4 -2 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-832,9536] |
[a1,a2,a3,a4,a6] |
Generators |
[-16:136:1] [10:46:1] |
Generators of the group modulo torsion |
j |
-15568817473/31211 |
j-invariant |
L |
5.4173380418673 |
L(r)(E,1)/r! |
Ω |
1.8559944107085 |
Real period |
R |
0.3648541457487 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
1357a1 86848w1 |
Quadratic twists by: -4 8 |