Atkin-Lehner |
3+ 7- 11- 29+ |
Signs for the Atkin-Lehner involutions |
Class |
73689m |
Isogeny class |
Conductor |
73689 |
Conductor |
∏ cp |
16 |
Product of Tamagawa factors cp |
deg |
2488320 |
Modular degree for the optimal curve |
Δ |
-9.3614777949849E+19 |
Discriminant |
Eigenvalues |
1 3+ -2 7- 11- -2 -2 8 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-4091496,-3220993629] |
[a1,a2,a3,a4,a6] |
Generators |
[1609270438485039438:495803104082161123953:16891507190312] |
Generators of the group modulo torsion |
j |
-4275768267198290017/52843101620463 |
j-invariant |
L |
4.6610893810842 |
L(r)(E,1)/r! |
Ω |
0.053037062543293 |
Real period |
R |
21.970906567313 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999959464 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
6699d1 |
Quadratic twists by: -11 |