E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 29400.cs
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
29400.cs1 |
29400bu4 |
[0,1,0,−3548008,−2573228512] |
2624033547076/324135 |
610146537840000000 |
[2] |
884736 |
2.4360
|
|
29400.cs2 |
29400bu2 |
[0,1,0,−240508,−33068512] |
3269383504/893025 |
420253992900000000 |
[2,2] |
442368 |
2.0894
|
|
29400.cs3 |
29400bu1 |
[0,1,0,−87383,9500238] |
2508888064/118125 |
3474322031250000 |
[2] |
221184 |
1.7428
|
Γ0(N)-optimal |
29400.cs4 |
29400bu3 |
[0,1,0,616992,−214858512] |
13799183324/18600435 |
−35013161237040000000 |
[2] |
884736 |
2.4360
|
|
The elliptic curves in class 29400.cs have
rank 1.
The elliptic curves in class 29400.cs 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 LMFDB numbering.
⎝⎜⎜⎛1244212242144241⎠⎟⎟⎞
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.