Atkin-Lehner |
2+ 3- 13+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
69264k |
Isogeny class |
Conductor |
69264 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
Δ |
4.5371722725941E+20 |
Discriminant |
Eigenvalues |
2+ 3- 0 4 6 13+ 2 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-24398399055,-1466864874069442] |
[a1,a2,a3,a4,a6] |
Generators |
[898555675214177438146144060234364155003749226053153897820457884376525208870788596543768595889451875594608459446:-231790708054991097306398344952635485211120575103135489543586370688521146233685941065327403703302955246969992184573:4214042009289791669937744838087836746526925469277049267667432062229104585796567718991784463665765277508568] |
Generators of the group modulo torsion |
j |
8606770235119240834099339906000/2431183702307373 |
j-invariant |
L |
8.3571478078002 |
L(r)(E,1)/r! |
Ω |
0.012079785486105 |
Real period |
R |
172.9572892129 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
34632e2 23088d2 |
Quadratic twists by: -4 -3 |