Atkin-Lehner |
3+ 7- 13- 47- |
Signs for the Atkin-Lehner involutions |
Class |
89817g |
Isogeny class |
Conductor |
89817 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
2677248 |
Modular degree for the optimal curve |
Δ |
-19117293278016843 = -1 · 33 · 79 · 132 · 473 |
Discriminant |
Eigenvalues |
0 3+ -4 7- -5 13- -7 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,-1,1,-2787675,1792419257] |
[a1,a2,a3,a4,a6] |
Generators |
[-1927:2229:1] [959:-306:1] |
Generators of the group modulo torsion |
j |
-59370120277884928/473744349 |
j-invariant |
L |
4.8626761410726 |
L(r)(E,1)/r! |
Ω |
0.34673989293074 |
Real period |
R |
1.1686656771112 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000066 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
89817j1 |
Quadratic twists by: -7 |