Atkin-Lehner |
2+ 3- 5+ 11+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
51150u |
Isogeny class |
Conductor |
51150 |
Conductor |
∏ cp |
40 |
Product of Tamagawa factors cp |
deg |
81920 |
Modular degree for the optimal curve |
Δ |
642188250000 = 24 · 35 · 56 · 11 · 312 |
Discriminant |
Eigenvalues |
2+ 3- 5+ -2 11+ -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,-2426,-25252] |
[a1,a2,a3,a4,a6] |
Generators |
[81:517:1] [-27:157:1] |
Generators of the group modulo torsion |
j |
100999381393/41100048 |
j-invariant |
L |
8.0380397090595 |
L(r)(E,1)/r! |
Ω |
0.70491046731776 |
Real period |
R |
1.1402922898345 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999984 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
2046f1 |
Quadratic twists by: 5 |