Show commands:
SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 111600fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111600.bw2 | 111600fb1 | \([0, 0, 0, -147675, -22405750]\) | \(-7633736209/230640\) | \(-10760739840000000\) | \([2]\) | \(737280\) | \(1.8540\) | \(\Gamma_0(N)\)-optimal |
| 111600.bw1 | 111600fb2 | \([0, 0, 0, -2379675, -1412941750]\) | \(31942518433489/27900\) | \(1301702400000000\) | \([2]\) | \(1474560\) | \(2.2006\) |
Rank
sage: E.rank()
The elliptic curves in class 111600fb have rank \(0\).
Complex multiplication
The elliptic curves in class 111600fb do not have complex multiplication.Modular form 111600.2.a.fb
sage: E.q_eigenform(10)
Isogeny matrix
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
