Atkin-Lehner |
2+ 3+ 7- 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984p |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
36 |
Product of Tamagawa factors cp |
deg |
1327104 |
Modular degree for the optimal curve |
Δ |
-4460215540547321856 = -1 · 226 · 33 · 79 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ -3 7- 0 -2 0 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,384223,-43961439] |
[a1,a2,a3,a4,a6] |
Generators |
[115:1316:1] [3097:175616:1] |
Generators of the group modulo torsion |
j |
23929451044753463/17014372026624 |
j-invariant |
L |
8.1191320876016 |
L(r)(E,1)/r! |
Ω |
0.13809536528058 |
Real period |
R |
1.6331572491184 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000008 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984cl1 2562f1 |
Quadratic twists by: -4 8 |