E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 42978.c
sage: E.isogeny_class().curves
LMFDB label |
Cremona label |
Weierstrass coefficients |
j-invariant |
Discriminant |
Torsion structure |
Modular degree |
Faltings height |
Optimality |
42978.c1 |
42978b4 |
[1,1,0,−16059278499,−783322981022457] |
458038307459437803276572539343003833/86000447460798 |
86000447460798 |
[2] |
40919040 |
3.9675
|
|
42978.c2 |
42978b2 |
[1,1,0,−1003704909,−12239735151735] |
111825759760338976846738658338393/1532291201797601099556 |
1532291201797601099556 |
[2,2] |
20459520 |
3.6209
|
|
42978.c3 |
42978b3 |
[1,1,0,−1002813239,−12262566362085] |
−111527993597885114164012178708473/413980765601504764798430334 |
−413980765601504764798430334 |
[2] |
40919040 |
3.9675
|
|
42978.c4 |
42978b1 |
[1,1,0,−62787289,−190908660587] |
27374041292637614212993237273/101051566314387812377488 |
101051566314387812377488 |
[2] |
10229760 |
3.2743
|
Γ0(N)-optimal |
The elliptic curves in class 42978.c have
rank 1.
The elliptic curves in class 42978.c 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.