Atkin-Lehner |
2+ 3+ 5+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
13200m |
Isogeny class |
Conductor |
13200 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-15468750000 = -1 · 24 · 32 · 510 · 11 |
Discriminant |
Eigenvalues |
2+ 3+ 5+ -4 11- -2 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,617,-1238] |
[a1,a2,a3,a4,a6] |
Generators |
[18:124:1] [22:150:1] |
Generators of the group modulo torsion |
j |
103737344/61875 |
j-invariant |
L |
5.3266527503221 |
L(r)(E,1)/r! |
Ω |
0.72555357472679 |
Real period |
R |
3.6707508141816 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6600l1 52800go1 39600v1 2640n1 |
Quadratic twists by: -4 8 -3 5 |