Atkin-Lehner |
2- 13+ 31+ |
Signs for the Atkin-Lehner involutions |
Class |
83824q |
Isogeny class |
Conductor |
83824 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
322560 |
Modular degree for the optimal curve |
Δ |
-7903815249035264 = -1 · 217 · 137 · 312 |
Discriminant |
Eigenvalues |
2- -1 -1 -3 0 13+ -5 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-6816,-4280576] |
[a1,a2,a3,a4,a6] |
Generators |
[490:10478:1] [178:338:1] |
Generators of the group modulo torsion |
j |
-1771561/399776 |
j-invariant |
L |
7.3381361957048 |
L(r)(E,1)/r! |
Ω |
0.18556237295163 |
Real period |
R |
2.4715868035796 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000074 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
10478j1 6448g1 |
Quadratic twists by: -4 13 |