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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 3520bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 3520.z1 | 3520bh1 | \([0, 1, 0, -5665, -167585]\) | \(-76711450249/851840\) | \(-223304744960\) | \([]\) | \(5376\) | \(0.99253\) | \(\Gamma_0(N)\)-optimal |
| 3520.z2 | 3520bh2 | \([0, 1, 0, 18975, -852577]\) | \(2882081488391/2883584000\) | \(-755914244096000\) | \([]\) | \(16128\) | \(1.5418\) |
Rank
sage: E.rank()
The elliptic curves in class 3520bh have rank \(0\).
Complex multiplication
The elliptic curves in class 3520bh do not have complex multiplication.Modular form 3520.2.a.bh
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
