Atkin-Lehner |
3+ 5- 13- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
48165m |
Isogeny class |
Conductor |
48165 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
244608 |
Modular degree for the optimal curve |
Δ |
-20729834441830995 = -1 · 3 · 5 · 139 · 194 |
Discriminant |
Eigenvalues |
0 3+ 5- 1 -1 13- -3 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-196265,-34110724] |
[a1,a2,a3,a4,a6] |
Generators |
[112591600:9538413788:15625] |
Generators of the group modulo torsion |
j |
-78843215872/1954815 |
j-invariant |
L |
3.8791247979543 |
L(r)(E,1)/r! |
Ω |
0.1132459034561 |
Real period |
R |
8.563499163284 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999678 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48165g1 |
Quadratic twists by: 13 |