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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 7488.bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 7488.bm1 | 7488bh2 | \([0, 0, 0, -204, -752]\) | \(530604/169\) | \(299040768\) | \([2]\) | \(2048\) | \(0.33013\) | |
| 7488.bm2 | 7488bh1 | \([0, 0, 0, 36, -80]\) | \(11664/13\) | \(-5750784\) | \([2]\) | \(1024\) | \(-0.016441\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 7488.bm have rank \(1\).
Complex multiplication
The elliptic curves in class 7488.bm do not have complex multiplication.Modular form 7488.2.a.bm
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.
