Atkin-Lehner |
3+ 11+ 19+ |
Signs for the Atkin-Lehner involutions |
Class |
20691a |
Isogeny class |
Conductor |
20691 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
5184 |
Modular degree for the optimal curve |
Δ |
12973257 = 33 · 113 · 192 |
Discriminant |
Eigenvalues |
1 3+ 0 -4 11+ -4 6 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-237,-1336] |
[a1,a2,a3,a4,a6] |
Generators |
[40:208:1] |
Generators of the group modulo torsion |
j |
41063625/361 |
j-invariant |
L |
4.5344577323938 |
L(r)(E,1)/r! |
Ω |
1.217186060162 |
Real period |
R |
1.8626806043895 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
20691b1 20691f1 |
Quadratic twists by: -3 -11 |