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SageMath
E = EllipticCurve("bh1")
E.isogeny_class()
Elliptic curves in class 42432.bh
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 42432.bh1 | 42432cc2 | \([0, -1, 0, -20961, 397953]\) | \(3885442650361/1996623837\) | \(523402959126528\) | \([2]\) | \(294912\) | \(1.5165\) | |
| 42432.bh2 | 42432cc1 | \([0, -1, 0, -16801, 843073]\) | \(2000852317801/2094417\) | \(549038850048\) | \([2]\) | \(147456\) | \(1.1699\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 42432.bh have rank \(0\).
Complex multiplication
The elliptic curves in class 42432.bh do not have complex multiplication.Modular form 42432.2.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 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.
