Atkin-Lehner |
2+ 3- 5- 19- |
Signs for the Atkin-Lehner involutions |
Class |
86640bh |
Isogeny class |
Conductor |
86640 |
Conductor |
∏ cp |
216 |
Product of Tamagawa factors cp |
deg |
311040 |
Modular degree for the optimal curve |
Δ |
-113689008000000 = -1 · 210 · 39 · 56 · 192 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 -2 -1 -8 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-21400,1302500] |
[a1,a2,a3,a4,a6] |
Generators |
[110:540:1] [-142:1224:1] |
Generators of the group modulo torsion |
j |
-2932095879364/307546875 |
j-invariant |
L |
12.694576914674 |
L(r)(E,1)/r! |
Ω |
0.57680042004597 |
Real period |
R |
0.10189172437821 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999998682 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
43320y1 86640g1 |
Quadratic twists by: -4 -19 |