Atkin-Lehner |
2- 89- |
Signs for the Atkin-Lehner involutions |
Class |
356a |
Isogeny class |
Conductor |
356 |
Conductor |
∏ cp |
3 |
Product of Tamagawa factors cp |
deg |
12 |
Modular degree for the optimal curve |
Δ |
-22784 = -1 · 28 · 89 |
Discriminant |
Eigenvalues |
2- -1 -1 0 0 -4 -1 -5 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,0,4,-8] |
[a1,a2,a3,a4,a6] |
Generators |
[2:2:1] |
Generators of the group modulo torsion |
j |
21296/89 |
j-invariant |
L |
1.473836667143 |
L(r)(E,1)/r! |
Ω |
1.9261487705605 |
Real period |
R |
0.25505760331519 |
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 |
1424d1 5696e1 3204c1 8900b1 |
Quadratic twists by: -4 8 -3 5 |