Atkin-Lehner |
2+ 3+ 7- 19+ 23+ |
Signs for the Atkin-Lehner involutions |
Class |
128478b |
Isogeny class |
Conductor |
128478 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1152000 |
Modular degree for the optimal curve |
Δ |
-201458760143929344 = -1 · 216 · 33 · 72 · 192 · 235 |
Discriminant |
Eigenvalues |
2+ 3+ -1 7- 0 -1 3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,19512,21577536] |
[a1,a2,a3,a4,a6] |
Generators |
[80:-4904:1] [631:16585:1] |
Generators of the group modulo torsion |
j |
16764793782997799/4111403268243456 |
j-invariant |
L |
7.5426699973362 |
L(r)(E,1)/r! |
Ω |
0.24558032841943 |
Real period |
R |
7.6784142708054 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.000000000514 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
128478ba1 |
Quadratic twists by: -7 |