Atkin-Lehner |
2+ 31+ 43+ |
Signs for the Atkin-Lehner involutions |
Class |
85312d |
Isogeny class |
Conductor |
85312 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
121856 |
Modular degree for the optimal curve |
Δ |
-108526418944 = -1 · 210 · 31 · 434 |
Discriminant |
Eigenvalues |
2+ 2 3 -3 -2 6 6 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1169,-21703] |
[a1,a2,a3,a4,a6] |
Generators |
[167274352280:1264967229177:2171747375] |
Generators of the group modulo torsion |
j |
-172678690048/105982831 |
j-invariant |
L |
12.03814173321 |
L(r)(E,1)/r! |
Ω |
0.39712039629754 |
Real period |
R |
15.156791045543 |
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 |
85312bb1 10664d1 |
Quadratic twists by: -4 8 |