Atkin-Lehner |
5+ 7- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
51205f |
Isogeny class |
Conductor |
51205 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
40320 |
Modular degree for the optimal curve |
Δ |
-27106646875 = -1 · 55 · 73 · 113 · 19 |
Discriminant |
Eigenvalues |
0 2 5+ 7- 11+ 5 2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,649,4507] |
[a1,a2,a3,a4,a6] |
Generators |
[-159:557:27] |
Generators of the group modulo torsion |
j |
88002363392/79028125 |
j-invariant |
L |
7.0613860609393 |
L(r)(E,1)/r! |
Ω |
0.77372815145335 |
Real period |
R |
4.5632216223007 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999291 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
51205m1 |
Quadratic twists by: -7 |