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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 360672bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 360672.bf1 | 360672bf1 | \([0, 1, 0, -838774, 295309052]\) | \(42246001231552/14414517\) | \(22267609516107072\) | \([2]\) | \(3538944\) | \(2.1084\) | \(\Gamma_0(N)\)-optimal |
| 360672.bf2 | 360672bf2 | \([0, 1, 0, -721729, 380775311]\) | \(-420526439488/390971529\) | \(-38654370849886212096\) | \([2]\) | \(7077888\) | \(2.4550\) |
Rank
sage: E.rank()
The elliptic curves in class 360672bf have rank \(1\).
Complex multiplication
The elliptic curves in class 360672bf do not have complex multiplication.Modular form 360672.2.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 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.
