Atkin-Lehner |
2+ 11+ 47+ |
Signs for the Atkin-Lehner involutions |
Class |
33088g |
Isogeny class |
Conductor |
33088 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
168960 |
Modular degree for the optimal curve |
Δ |
-5828799021056 = -1 · 214 · 115 · 472 |
Discriminant |
Eigenvalues |
2+ 3 1 -4 11+ 4 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-27472,1756448] |
[a1,a2,a3,a4,a6] |
Generators |
[30534:180433:216] |
Generators of the group modulo torsion |
j |
-139950548941824/355761659 |
j-invariant |
L |
9.6187700975155 |
L(r)(E,1)/r! |
Ω |
0.76031943132665 |
Real period |
R |
6.3254795952878 |
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 |
33088bn1 4136b1 |
Quadratic twists by: -4 8 |