Atkin-Lehner |
3- 7+ 11- |
Signs for the Atkin-Lehner involutions |
Class |
693b |
Isogeny class |
Conductor |
693 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
56 |
Modular degree for the optimal curve |
Δ |
-392931 = -1 · 36 · 72 · 11 |
Discriminant |
Eigenvalues |
0 3- 1 7+ 11- -4 -2 -6 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,1,18,-7] |
[a1,a2,a3,a4,a6] |
Generators |
[1:3:1] |
Generators of the group modulo torsion |
j |
884736/539 |
j-invariant |
L |
1.9629786598203 |
L(r)(E,1)/r! |
Ω |
1.7403153565852 |
Real period |
R |
0.56397211355761 |
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 |
11088bq1 44352u1 77a1 17325be1 |
Quadratic twists by: -4 8 -3 5 |