Atkin-Lehner |
2+ 7- 19- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
61712d |
Isogeny class |
Conductor |
61712 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
82944 |
Modular degree for the optimal curve |
Δ |
-1261227398144 = -1 · 210 · 76 · 192 · 29 |
Discriminant |
Eigenvalues |
2+ -1 3 7- 1 3 -2 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,-1384,58016] |
[a1,a2,a3,a4,a6] |
Generators |
[-10:266:1] |
Generators of the group modulo torsion |
j |
-286513958308/1231667381 |
j-invariant |
L |
6.6600976248619 |
L(r)(E,1)/r! |
Ω |
0.7500283905249 |
Real period |
R |
0.36999141794109 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998631 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
30856a1 |
Quadratic twists by: -4 |