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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 10944.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10944.bf1 | 10944l3 | \([0, 0, 0, -49260, 33849776]\) | \(-69173457625/2550136832\) | \(-487338737802412032\) | \([]\) | \(103680\) | \(2.0742\) | |
| 10944.bf2 | 10944l1 | \([0, 0, 0, -8940, -325456]\) | \(-413493625/152\) | \(-29047652352\) | \([]\) | \(11520\) | \(0.97558\) | \(\Gamma_0(N)\)-optimal |
| 10944.bf3 | 10944l2 | \([0, 0, 0, 5460, -1236688]\) | \(94196375/3511808\) | \(-671116959940608\) | \([]\) | \(34560\) | \(1.5249\) |
Rank
sage: E.rank()
The elliptic curves in class 10944.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 10944.bf do not have complex multiplication.Modular form 10944.2.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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
