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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 4032.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4032.bf1 | 4032a2 | \([0, 0, 0, -444, 3600]\) | \(21882096/7\) | \(3096576\) | \([2]\) | \(1024\) | \(0.22027\) | |
| 4032.bf2 | 4032a1 | \([0, 0, 0, -24, 72]\) | \(-55296/49\) | \(-1354752\) | \([2]\) | \(512\) | \(-0.12630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4032.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 4032.bf do not have complex multiplication.Modular form 4032.2.a.bf
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 LMFDB 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 LMFDB labels.
