Atkin-Lehner |
2+ 3- 7- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
67032u |
Isogeny class |
Conductor |
67032 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
9216 |
Modular degree for the optimal curve |
Δ |
-10859184 = -1 · 24 · 36 · 72 · 19 |
Discriminant |
Eigenvalues |
2+ 3- -1 7- -3 2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,42,-119] |
[a1,a2,a3,a4,a6] |
Generators |
[8:27:1] |
Generators of the group modulo torsion |
j |
14336/19 |
j-invariant |
L |
5.1909570695013 |
L(r)(E,1)/r! |
Ω |
1.214038675509 |
Real period |
R |
1.0689439253931 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999822 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
7448u1 67032l1 |
Quadratic twists by: -3 -7 |