Atkin-Lehner |
2- 3+ 5- 19+ |
Signs for the Atkin-Lehner involutions |
Class |
68400dw |
Isogeny class |
Conductor |
68400 |
Conductor |
∏ cp |
32 |
Product of Tamagawa factors cp |
deg |
491520 |
Modular degree for the optimal curve |
Δ |
-56844504000000000 = -1 · 212 · 39 · 59 · 192 |
Discriminant |
Eigenvalues |
2- 3+ 5- -2 -2 -2 -2 19+ |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-340875,77456250] |
[a1,a2,a3,a4,a6] |
Generators |
[325:-1000:1] |
Generators of the group modulo torsion |
j |
-27818127/361 |
j-invariant |
L |
4.8161514333608 |
L(r)(E,1)/r! |
Ω |
0.3538726728551 |
Real period |
R |
1.7012303443 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000001502 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
4275c1 68400dv1 68400du1 |
Quadratic twists by: -4 -3 5 |