Atkin-Lehner |
2+ 3- 11- 89- |
Signs for the Atkin-Lehner involutions |
Class |
64614h |
Isogeny class |
Conductor |
64614 |
Conductor |
∏ cp |
22 |
Product of Tamagawa factors cp |
deg |
118272 |
Modular degree for the optimal curve |
Δ |
-488370187008 = -1 · 28 · 311 · 112 · 89 |
Discriminant |
Eigenvalues |
2+ 3- -2 2 11- -4 -6 0 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,0,1,998,31436] |
[a1,a2,a3,a4,a6] |
Generators |
[13:-223:1] [-8:155:1] |
Generators of the group modulo torsion |
j |
909819760223/4036117248 |
j-invariant |
L |
8.5018380849 |
L(r)(E,1)/r! |
Ω |
0.66743416889771 |
Real period |
R |
0.5790041979962 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
0.99999999999844 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64614r1 |
Quadratic twists by: -11 |