Atkin-Lehner |
2- 3+ 11+ 23- |
Signs for the Atkin-Lehner involutions |
Class |
69828f |
Isogeny class |
Conductor |
69828 |
Conductor |
∏ cp |
1 |
Product of Tamagawa factors cp |
deg |
19593792 |
Modular degree for the optimal curve |
Δ |
1.1392990324124E+26 |
Discriminant |
Eigenvalues |
2- 3+ -2 0 11+ 4 7 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-121544274,47836559493] |
[a1,a2,a3,a4,a6] |
Generators |
[51405997251758622071679675528283116120480790830605658283259050121:5138373030345855616602797309861887699844649819921009076230139785283:134558996396676917707436967591375554383481148956133154224740131] |
Generators of the group modulo torsion |
j |
299591084078848/171885556953 |
j-invariant |
L |
5.2953339394454 |
L(r)(E,1)/r! |
Ω |
0.050586930017037 |
Real period |
R |
104.67790667791 |
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 |
69828o1 |
Quadratic twists by: -23 |