Atkin-Lehner |
2+ 3+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
23232m |
Isogeny class |
Conductor |
23232 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18432 |
Modular degree for the optimal curve |
Δ |
-10277093376 = -1 · 220 · 34 · 112 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -4 11- -5 -7 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-865,11233] |
[a1,a2,a3,a4,a6] |
Generators |
[-17:144:1] [9:64:1] |
Generators of the group modulo torsion |
j |
-2259169/324 |
j-invariant |
L |
6.4182897862995 |
L(r)(E,1)/r! |
Ω |
1.243671993945 |
Real period |
R |
0.64509470921064 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000001 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
23232dn1 726d1 69696cc1 23232l1 |
Quadratic twists by: -4 8 -3 -11 |