Atkin-Lehner |
2+ 3+ 7- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
27048b |
Isogeny class |
Conductor |
27048 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
274176 |
Modular degree for the optimal curve |
Δ |
-21125561963127552 = -1 · 28 · 321 · 73 · 23 |
Discriminant |
Eigenvalues |
2+ 3+ 4 7- -1 0 6 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-67601,9752373] |
[a1,a2,a3,a4,a6] |
j |
-389094786976768/240588123669 |
j-invariant |
L |
2.8349860542018 |
L(r)(E,1)/r! |
Ω |
0.35437325677524 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
54096v1 81144cf1 27048h1 |
Quadratic twists by: -4 -3 -7 |