Atkin-Lehner |
2- 7- 13+ 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68614x |
Isogeny class |
Conductor |
68614 |
Conductor |
∏ cp |
27 |
Product of Tamagawa factors cp |
deg |
247104 |
Modular degree for the optimal curve |
Δ |
-84783788217856 = -1 · 29 · 7 · 138 · 29 |
Discriminant |
Eigenvalues |
2- -2 -3 7- -3 13+ -3 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,8193,339481] |
[a1,a2,a3,a4,a6] |
Generators |
[-34:165:1] |
Generators of the group modulo torsion |
j |
74559407/103936 |
j-invariant |
L |
4.0755589869043 |
L(r)(E,1)/r! |
Ω |
0.40998318493915 |
Real period |
R |
3.3135984892394 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000541 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
68614c1 |
Quadratic twists by: 13 |