Atkin-Lehner |
2- 3+ 7- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
68208bd |
Isogeny class |
Conductor |
68208 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
75264 |
Modular degree for the optimal curve |
Δ |
-1516649965488 = -1 · 24 · 34 · 79 · 29 |
Discriminant |
Eigenvalues |
2- 3+ 0 7- -2 0 -2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,2287,40944] |
[a1,a2,a3,a4,a6] |
Generators |
[61000:722331:512] |
Generators of the group modulo torsion |
j |
2048000/2349 |
j-invariant |
L |
4.5643345924746 |
L(r)(E,1)/r! |
Ω |
0.56526297541594 |
Real period |
R |
8.07470998567 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000776 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
17052k1 68208ci1 |
Quadratic twists by: -4 -7 |