Atkin-Lehner |
2+ 3- 11+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
120384bb |
Isogeny class |
Conductor |
120384 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
691200 |
Modular degree for the optimal curve |
Δ |
-3216230503022592 = -1 · 217 · 36 · 116 · 19 |
Discriminant |
Eigenvalues |
2+ 3- 2 -3 11+ 1 7 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-186924,-31225552] |
[a1,a2,a3,a4,a6] |
Generators |
[326489609032:54539712220268:11697083] |
Generators of the group modulo torsion |
j |
-7559297810066/33659659 |
j-invariant |
L |
7.7152934741408 |
L(r)(E,1)/r! |
Ω |
0.11477243347478 |
Real period |
R |
16.80563276511 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
120384di1 15048g1 13376j1 |
Quadratic twists by: -4 8 -3 |