Atkin-Lehner |
3+ 19- 61- |
Signs for the Atkin-Lehner involutions |
Class |
3477a |
Isogeny class |
Conductor |
3477 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
1680 |
Modular degree for the optimal curve |
Δ |
-1931748183 = -1 · 35 · 194 · 61 |
Discriminant |
Eigenvalues |
1 3+ -2 0 -4 6 6 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,189,1944] |
[a1,a2,a3,a4,a6] |
Generators |
[278:1685:8] |
Generators of the group modulo torsion |
j |
740480746823/1931748183 |
j-invariant |
L |
3.1041910712808 |
L(r)(E,1)/r! |
Ω |
1.0349921860151 |
Real period |
R |
2.9992410698603 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
55632w1 10431b1 86925l1 66063h1 |
Quadratic twists by: -4 -3 5 -19 |