Atkin-Lehner |
23+ 59+ |
Signs for the Atkin-Lehner involutions |
Class |
1357a |
Isogeny class |
Conductor |
1357 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
112 |
Modular degree for the optimal curve |
Δ |
-31211 = -1 · 232 · 59 |
Discriminant |
Eigenvalues |
-1 1 -3 1 0 4 -2 7 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,-52,-149] |
[a1,a2,a3,a4,a6] |
Generators |
[9:7:1] |
Generators of the group modulo torsion |
j |
-15568817473/31211 |
j-invariant |
L |
1.8062341392833 |
L(r)(E,1)/r! |
Ω |
0.8887365900296 |
Real period |
R |
1.0161808119226 |
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 |
21712j1 86848e1 12213b1 33925c1 |
Quadratic twists by: -4 8 -3 5 |