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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 106560bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.be2 | 106560bh1 | \([0, 0, 0, -6528, 78752]\) | \(2575826944/1266325\) | \(15124904755200\) | \([]\) | \(138240\) | \(1.2222\) | \(\Gamma_0(N)\)-optimal |
| 106560.be1 | 106560bh2 | \([0, 0, 0, -432768, 109579808]\) | \(750484394082304/578125\) | \(6905088000000\) | \([]\) | \(414720\) | \(1.7715\) |
Rank
sage: E.rank()
The elliptic curves in class 106560bh have rank \(0\).
Complex multiplication
The elliptic curves in class 106560bh do not have complex multiplication.Modular form 106560.2.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.
