Atkin-Lehner |
3+ 5+ 17- 67- |
Signs for the Atkin-Lehner involutions |
Class |
17085a |
Isogeny class |
Conductor |
17085 |
Conductor |
∏ cp |
6 |
Product of Tamagawa factors cp |
deg |
50688 |
Modular degree for the optimal curve |
Δ |
-53925866015625 = -1 · 33 · 58 · 17 · 673 |
Discriminant |
Eigenvalues |
1 3+ 5+ -2 -1 -4 17- -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-23973,-1481742] |
[a1,a2,a3,a4,a6] |
Generators |
[206:1438:1] |
Generators of the group modulo torsion |
j |
-1523769141358870489/53925866015625 |
j-invariant |
L |
3.317920786444 |
L(r)(E,1)/r! |
Ω |
0.19144076355149 |
Real period |
R |
2.8885530306189 |
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 |
51255e1 85425m1 |
Quadratic twists by: -3 5 |