Atkin-Lehner |
3+ 5+ 13- 19- |
Signs for the Atkin-Lehner involutions |
Class |
48165g |
Isogeny class |
Conductor |
48165 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
18816 |
Modular degree for the optimal curve |
Δ |
-4294728555 = -1 · 3 · 5 · 133 · 194 |
Discriminant |
Eigenvalues |
0 3+ 5+ -1 1 13- -3 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-1161,-15169] |
[a1,a2,a3,a4,a6] |
Generators |
[61:370:1] |
Generators of the group modulo torsion |
j |
-78843215872/1954815 |
j-invariant |
L |
2.9286198701246 |
L(r)(E,1)/r! |
Ω |
0.40831391164723 |
Real period |
R |
0.8965589300861 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999962 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48165m1 |
Quadratic twists by: 13 |