Atkin-Lehner |
2- 7+ 17- 37+ |
Signs for the Atkin-Lehner involutions |
Class |
61642p |
Isogeny class |
Conductor |
61642 |
Conductor |
∏ cp |
84 |
Product of Tamagawa factors cp |
deg |
733824 |
Modular degree for the optimal curve |
Δ |
-635264331800526848 = -1 · 214 · 78 · 173 · 372 |
Discriminant |
Eigenvalues |
2- 1 0 7+ 5 -1 17- -2 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,0,23617,38323865] |
[a1,a2,a3,a4,a6] |
Generators |
[-202:5133:1] |
Generators of the group modulo torsion |
j |
252704183375/110197096448 |
j-invariant |
L |
11.855115500389 |
L(r)(E,1)/r! |
Ω |
0.22419664824077 |
Real period |
R |
0.62950239662419 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000206 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
61642r1 |
Quadratic twists by: -7 |