Atkin-Lehner |
2- 3+ 5- 7+ 17+ |
Signs for the Atkin-Lehner involutions |
Class |
74970ce |
Isogeny class |
Conductor |
74970 |
Conductor |
∏ cp |
54 |
Product of Tamagawa factors cp |
deg |
169344 |
Modular degree for the optimal curve |
Δ |
-2646043659000 = -1 · 23 · 33 · 53 · 78 · 17 |
Discriminant |
Eigenvalues |
2- 3+ 5- 7+ 0 5 17+ -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,1,-9197,350669] |
[a1,a2,a3,a4,a6] |
Generators |
[-3:616:1] |
Generators of the group modulo torsion |
j |
-552675123/17000 |
j-invariant |
L |
11.935873933754 |
L(r)(E,1)/r! |
Ω |
0.80639848129147 |
Real period |
R |
2.4669098074631 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000358 |
(Analytic) order of Ш |
t |
3 |
Number of elements in the torsion subgroup |
Twists |
74970a2 74970bz1 |
Quadratic twists by: -3 -7 |