Atkin-Lehner |
2- 3+ 23+ 61- |
Signs for the Atkin-Lehner involutions |
Class |
67344l |
Isogeny class |
Conductor |
67344 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
721920 |
Modular degree for the optimal curve |
Δ |
-7916034400321536 = -1 · 217 · 316 · 23 · 61 |
Discriminant |
Eigenvalues |
2- 3+ 1 -3 2 6 6 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-406040,99814128] |
[a1,a2,a3,a4,a6] |
Generators |
[41770:144342:125] |
Generators of the group modulo torsion |
j |
-1807470804711985561/1932625586016 |
j-invariant |
L |
5.5872926675644 |
L(r)(E,1)/r! |
Ω |
0.41383942410472 |
Real period |
R |
3.3752781532176 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999983554 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
8418b1 |
Quadratic twists by: -4 |