E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 19110p
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
19110.e3 |
19110p1 |
[1,1,0,−6805617032,−216099982943424] |
296304326013275547793071733369/268420373544960000000 |
31579388527190999040000000 |
[2] |
20643840 |
4.1911
|
Γ0(N)-optimal |
19110.e2 |
19110p2 |
[1,1,0,−6854789512,−212818772194496] |
302773487204995438715379645049/8911747415025000000000000 |
1048458171630276225000000000000 |
[2,2] |
41287680 |
4.5377
|
|
19110.e1 |
19110p3 |
[1,1,0,−16216549192,494082084186496] |
4008766897254067912673785886329/1423480510711669921875000000 |
167471058604717254638671875000000 |
[4] |
82575360 |
4.8843
|
|
19110.e4 |
19110p4 |
[1,1,0,1720210488,−709721157194496] |
4784981304203817469820354951/1852343836482910078035000000 |
−217926400018377887770739715000000 |
[2] |
82575360 |
4.8843
|
|
The elliptic curves in class 19110p have
rank 0.
The elliptic curves in class 19110p do not have complex multiplication.
sage: E.isogeny_class().matrix()
The i,j entry is the smallest degree of a cyclic isogeny between the i-th and j-th curve in the isogeny class, in the Cremona numbering.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.