Atkin-Lehner |
2+ 3+ 7+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
81984c |
Isogeny class |
Conductor |
81984 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
414720 |
Modular degree for the optimal curve |
Δ |
-562525421617152 = -1 · 214 · 32 · 75 · 613 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7+ 0 -4 -3 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1701,-1140867] |
[a1,a2,a3,a4,a6] |
Generators |
[513888540:9219440319:1520875] |
Generators of the group modulo torsion |
j |
-33240841216/34333827003 |
j-invariant |
L |
6.9905711301893 |
L(r)(E,1)/r! |
Ω |
0.23378487511669 |
Real period |
R |
14.950862680276 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001429 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
81984co1 10248c1 |
Quadratic twists by: -4 8 |