Atkin-Lehner |
2- 5+ 19- 47- |
Signs for the Atkin-Lehner involutions |
Class |
89300g |
Isogeny class |
Conductor |
89300 |
Conductor |
∏ cp |
8 |
Product of Tamagawa factors cp |
deg |
179712 |
Modular degree for the optimal curve |
Δ |
-8483500000000 = -1 · 28 · 59 · 192 · 47 |
Discriminant |
Eigenvalues |
2- 0 5+ -4 -6 3 0 19- |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-3200,156500] |
[a1,a2,a3,a4,a6] |
Generators |
[-35:475:1] [5:375:1] |
Generators of the group modulo torsion |
j |
-905969664/2120875 |
j-invariant |
L |
9.0213962992021 |
L(r)(E,1)/r! |
Ω |
0.65117416277466 |
Real period |
R |
1.7317556528115 |
Regulator |
r |
2 |
Rank of the group of rational points |
S |
1.0000000000447 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
17860b1 |
Quadratic twists by: 5 |