Atkin-Lehner |
2- 3+ 5+ 17+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
19380d |
Isogeny class |
Conductor |
19380 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
13824 |
Modular degree for the optimal curve |
Δ |
80529714000 = 24 · 38 · 53 · 17 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 5+ 0 -2 4 17+ 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1221,-8730] |
[a1,a2,a3,a4,a6] |
Generators |
[-11:57:1] |
Generators of the group modulo torsion |
j |
12592337649664/5033107125 |
j-invariant |
L |
3.9408744677493 |
L(r)(E,1)/r! |
Ω |
0.83597384407444 |
Real period |
R |
1.5713707215774 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
77520cc1 58140r1 96900bf1 |
Quadratic twists by: -4 -3 5 |