E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 343824ca
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
343824.ca4 |
343824ca1 |
[0,1,0,−1004596632,12216145084308] |
27374041292637614212993237273/101051566314387812377488 |
413907215623732479498190848 |
[2] |
245514240 |
3.9675
|
Γ0(N)-optimal |
343824.ca2 |
343824ca2 |
[0,1,0,−16059278552,783310931153940] |
111825759760338976846738658338393/1532291201797601099556 |
6276264762562974103781376 |
[2,2] |
491028480 |
4.3140
|
|
343824.ca1 |
343824ca3 |
[0,1,0,−256948455992,50132156888525268] |
458038307459437803276572539343003833/86000447460798 |
352257832799428608 |
[2] |
982056960 |
4.6606
|
|
343824.ca3 |
343824ca4 |
[0,1,0,−16045011832,784772157149780] |
−111527993597885114164012178708473/413980765601504764798430334 |
−1695665215903763516614370648064 |
[2] |
982056960 |
4.6606
|
|
The elliptic curves in class 343824ca have
rank 0.
The elliptic curves in class 343824ca 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.