Atkin-Lehner |
2+ 11- 67- |
Signs for the Atkin-Lehner involutions |
Class |
129712i |
Isogeny class |
Conductor |
129712 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
418176 |
Modular degree for the optimal curve |
Δ |
-1031539522019248 = -1 · 24 · 118 · 673 |
Discriminant |
Eigenvalues |
2+ 0 0 2 11- 6 6 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-13310,-1654433] |
[a1,a2,a3,a4,a6] |
Generators |
[1706190195:16065228242:8615125] |
Generators of the group modulo torsion |
j |
-76032000/300763 |
j-invariant |
L |
8.2139450766847 |
L(r)(E,1)/r! |
Ω |
0.20290342892928 |
Real period |
R |
13.49401383645 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000005403 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
64856b1 129712j1 |
Quadratic twists by: -4 -11 |