Atkin-Lehner |
2+ 3- 17- 31+ |
Signs for the Atkin-Lehner involutions |
Class |
12648d |
Isogeny class |
Conductor |
12648 |
Conductor |
∏ cp |
72 |
Product of Tamagawa factors cp |
deg |
21888 |
Modular degree for the optimal curve |
Δ |
-8727758749296 = -1 · 24 · 36 · 176 · 31 |
Discriminant |
Eigenvalues |
2+ 3- 1 3 -2 -2 17- 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,0,-3060,-157383] |
[a1,a2,a3,a4,a6] |
Generators |
[396:-7803:1] |
Generators of the group modulo torsion |
j |
-198111610045696/545484921831 |
j-invariant |
L |
6.4961819201239 |
L(r)(E,1)/r! |
Ω |
0.2977525111405 |
Real period |
R |
0.30301927108865 |
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 |
25296e1 101184h1 37944j1 |
Quadratic twists by: -4 8 -3 |