Atkin-Lehner |
3+ 5- 7+ 31- |
Signs for the Atkin-Lehner involutions |
Class |
68355f |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2193408 |
Modular degree for the optimal curve |
Δ |
1374033562723828125 = 39 · 58 · 78 · 31 |
Discriminant |
Eigenvalues |
2 3+ 5- 7+ -5 -2 -3 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-990927,375461777] |
[a1,a2,a3,a4,a6] |
Generators |
[5826:50621:8] |
Generators of the group modulo torsion |
j |
948359688192/12109375 |
j-invariant |
L |
12.42386721775 |
L(r)(E,1)/r! |
Ω |
0.27135752952453 |
Real period |
R |
2.8615078510152 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999992639 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68355b1 68355d1 |
Quadratic twists by: -3 -7 |