Atkin-Lehner |
2+ 7- 17+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
61642i |
Isogeny class |
Conductor |
61642 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
784896 |
Modular degree for the optimal curve |
Δ |
-65394857685348352 = -1 · 212 · 79 · 172 · 372 |
Discriminant |
Eigenvalues |
2+ 0 2 7- 4 -6 17+ -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,-1,0,-268676,55064400] |
[a1,a2,a3,a4,a6] |
Generators |
[-267:10512:1] |
Generators of the group modulo torsion |
j |
-53153134832799/1620545536 |
j-invariant |
L |
4.5988420686147 |
L(r)(E,1)/r! |
Ω |
0.34715087844763 |
Real period |
R |
3.311846774627 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000504 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
61642k1 |
Quadratic twists by: -7 |