Atkin-Lehner |
3+ 5+ 13- 17- |
Signs for the Atkin-Lehner involutions |
Class |
3315c |
Isogeny class |
Conductor |
3315 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
59904 |
Modular degree for the optimal curve |
Δ |
-2615843353271484375 = -1 · 33 · 516 · 133 · 172 |
Discriminant |
Eigenvalues |
1 3+ 5+ 4 -4 13- 17- 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,226942,65848887] |
[a1,a2,a3,a4,a6] |
Generators |
[33470:1493137:125] |
Generators of the group modulo torsion |
j |
1292603583867446566871/2615843353271484375 |
j-invariant |
L |
3.587221336764 |
L(r)(E,1)/r! |
Ω |
0.17717111506143 |
Real period |
R |
6.7490710614616 |
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 |
53040cp1 9945j1 16575g1 43095h1 |
Quadratic twists by: -4 -3 5 13 |