Atkin-Lehner |
2- 3+ 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400dt |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
32768 |
Modular degree for the optimal curve |
Δ |
-4990464000 = -1 · 212 · 33 · 53 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 5- 2 2 2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-1515,-22950] |
[a1,a2,a3,a4,a6] |
Generators |
[85:680:1] |
Generators of the group modulo torsion |
j |
-27818127/361 |
j-invariant |
L |
7.6057534081459 |
L(r)(E,1)/r! |
Ω |
0.38232349753968 |
Real period |
R |
2.4866877976331 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999993467 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4275d1 68400du1 68400dv1 |
Quadratic twists by: -4 -3 5 |