Atkin-Lehner |
5+ 11- 61- |
Signs for the Atkin-Lehner involutions |
Class |
3355a |
Isogeny class |
Conductor |
3355 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
408 |
Modular degree for the optimal curve |
Δ |
-405955 = -1 · 5 · 113 · 61 |
Discriminant |
Eigenvalues |
0 -2 5+ -4 11- -1 0 2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,1,1,-11,30] |
[a1,a2,a3,a4,a6] |
Generators |
[2:4:1] |
Generators of the group modulo torsion |
j |
-160989184/405955 |
j-invariant |
L |
1.391341291622 |
L(r)(E,1)/r! |
Ω |
2.6468533994733 |
Real period |
R |
1.5769758444864 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
53680r1 30195o1 16775b1 36905a1 |
Quadratic twists by: -4 -3 5 -11 |