Atkin-Lehner |
2+ 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
51984f |
Isogeny class |
Conductor |
51984 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
11520 |
Modular degree for the optimal curve |
Δ |
-9980928 = -1 · 210 · 33 · 192 |
Discriminant |
Eigenvalues |
2+ 3+ -2 -3 -6 1 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-171,874] |
[a1,a2,a3,a4,a6] |
Generators |
[5:-12:1] [-13:30:1] |
Generators of the group modulo torsion |
j |
-55404 |
j-invariant |
L |
7.5963984525345 |
L(r)(E,1)/r! |
Ω |
2.2953640379474 |
Real period |
R |
0.4136815733228 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000002 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
25992c1 51984e1 51984b1 |
Quadratic twists by: -4 -3 -19 |