Atkin-Lehner |
2- 3+ 19- |
Signs for the Atkin-Lehner involutions |
Class |
69312cm |
Isogeny class |
Conductor |
69312 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
829440 |
Modular degree for the optimal curve |
Δ |
404910339520462848 = 224 · 33 · 197 |
Discriminant |
Eigenvalues |
2- 3+ 0 4 0 -4 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-185313,2407041] |
[a1,a2,a3,a4,a6] |
Generators |
[-23732245:12490647652:7189057] |
Generators of the group modulo torsion |
j |
57066625/32832 |
j-invariant |
L |
6.6248220119116 |
L(r)(E,1)/r! |
Ω |
0.25540714101928 |
Real period |
R |
12.969140144535 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000488 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
69312bo1 17328be1 3648bh1 |
Quadratic twists by: -4 8 -19 |