Atkin-Lehner |
2+ 3+ 7- 89- |
Signs for the Atkin-Lehner involutions |
Class |
89712b |
Isogeny class |
Conductor |
89712 |
Conductor |
∏ cp |
24 |
Product of Tamagawa factors cp |
deg |
181248 |
Modular degree for the optimal curve |
Δ |
-11699462492928 = -1 · 28 · 33 · 74 · 893 |
Discriminant |
Eigenvalues |
2+ 3+ -2 7- 2 -4 6 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-4476,-200916] |
[a1,a2,a3,a4,a6] |
Generators |
[321:5607:1] |
Generators of the group modulo torsion |
j |
-1434796194816/1692630569 |
j-invariant |
L |
6.0103754917798 |
L(r)(E,1)/r! |
Ω |
0.2791794209426 |
Real period |
R |
0.89702998632679 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.0000000000265 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
44856a1 89712a1 |
Quadratic twists by: -4 -3 |