Atkin-Lehner |
3- 5+ 43- |
Signs for the Atkin-Lehner involutions |
Class |
3225i |
Isogeny class |
Conductor |
3225 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
64512 |
Modular degree for the optimal curve |
Δ |
-148546686048046875 = -1 · 314 · 58 · 433 |
Discriminant |
Eigenvalues |
-2 3- 5+ 0 5 -1 -5 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-419508,106073894] |
[a1,a2,a3,a4,a6] |
Generators |
[-387:14512:1] |
Generators of the group modulo torsion |
j |
-522547125460258816/9506987907075 |
j-invariant |
L |
2.2289871629635 |
L(r)(E,1)/r! |
Ω |
0.32591140982145 |
Real period |
R |
0.081419553486601 |
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 |
51600bn1 9675p1 645c1 |
Quadratic twists by: -4 -3 5 |