Atkin-Lehner |
2+ 3+ 13+ 61+ |
Signs for the Atkin-Lehner involutions |
Class |
61854b |
Isogeny class |
Conductor |
61854 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
786240 |
Modular degree for the optimal curve |
Δ |
-60086406262237056 = -1 · 27 · 313 · 136 · 61 |
Discriminant |
Eigenvalues |
2+ 3+ 1 -2 -2 13+ 1 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-1199227,-506113187] |
[a1,a2,a3,a4,a6] |
Generators |
[2396375772090:256485427917179:205379000] |
Generators of the group modulo torsion |
j |
-39515579724486529/12448473984 |
j-invariant |
L |
2.8294603458681 |
L(r)(E,1)/r! |
Ω |
0.072133325600682 |
Real period |
R |
19.612712448138 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
366d1 |
Quadratic twists by: 13 |