Atkin-Lehner |
2- 5+ 11+ 89- |
Signs for the Atkin-Lehner involutions |
Class |
78320x |
Isogeny class |
Conductor |
78320 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
5529600 |
Modular degree for the optimal curve |
Δ |
110274560000000000 = 220 · 510 · 112 · 89 |
Discriminant |
Eigenvalues |
2- 0 5+ -2 11+ -4 -2 -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-289712603,-1898013057398] |
[a1,a2,a3,a4,a6] |
Generators |
[19049128906656741:3723800283163600000:418676865641] |
Generators of the group modulo torsion |
j |
656547162459736668851166129/26922500000000 |
j-invariant |
L |
3.2151398034404 |
L(r)(E,1)/r! |
Ω |
0.036593816640005 |
Real period |
R |
21.965048319131 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000002252 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
9790m1 |
Quadratic twists by: -4 |