Atkin-Lehner |
3+ 7- 47- |
Signs for the Atkin-Lehner involutions |
Class |
6909d |
Isogeny class |
Conductor |
6909 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
2304 |
Modular degree for the optimal curve |
Δ |
-447889743 = -1 · 34 · 76 · 47 |
Discriminant |
Eigenvalues |
-1 3+ -2 7- 4 2 -2 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,1,-99,-1128] |
[a1,a2,a3,a4,a6] |
Generators |
[20:63:1] |
Generators of the group modulo torsion |
j |
-912673/3807 |
j-invariant |
L |
1.9053402383287 |
L(r)(E,1)/r! |
Ω |
0.68916476066874 |
Real period |
R |
1.3823546610826 |
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 |
110544ds1 20727k1 141c1 |
Quadratic twists by: -4 -3 -7 |