Atkin-Lehner |
3+ 5- 7- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
68355h |
Isogeny class |
Conductor |
68355 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
104448 |
Modular degree for the optimal curve |
Δ |
16020703125 = 33 · 58 · 72 · 31 |
Discriminant |
Eigenvalues |
-2 3+ 5- 7- 5 2 -3 -7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,-2247,40542] |
[a1,a2,a3,a4,a6] |
Generators |
[32:-38:1] |
Generators of the group modulo torsion |
j |
948359688192/12109375 |
j-invariant |
L |
3.7510467580309 |
L(r)(E,1)/r! |
Ω |
1.2435164194424 |
Real period |
R |
0.18853021854496 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002355 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
68355d1 68355b1 |
Quadratic twists by: -3 -7 |