Atkin-Lehner |
3- 7+ 19- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
34713f |
Isogeny class |
Conductor |
34713 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
24192 |
Modular degree for the optimal curve |
Δ |
-135000696789 = -1 · 36 · 72 · 194 · 29 |
Discriminant |
Eigenvalues |
-1 3- -1 7+ 3 -1 -4 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-3278,75178] |
[a1,a2,a3,a4,a6] |
Generators |
[38:47:1] |
Generators of the group modulo torsion |
j |
-5341937695641/185186141 |
j-invariant |
L |
2.6692923134545 |
L(r)(E,1)/r! |
Ω |
1.0317372251655 |
Real period |
R |
0.32339779068097 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999986 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
3857a1 |
Quadratic twists by: -3 |