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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 333270bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 333270.bm1 | 333270bm1 | \([1, -1, 0, -722184, 201669488]\) | \(14295828483/2254000\) | \(6567683568783498000\) | \([2]\) | \(7299072\) | \(2.3335\) | \(\Gamma_0(N)\)-optimal |
| 333270.bm2 | 333270bm2 | \([1, -1, 0, 1277436, 1118695220]\) | \(79119341757/231437500\) | \(-674360366437591312500\) | \([2]\) | \(14598144\) | \(2.6801\) |
Rank
sage: E.rank()
The elliptic curves in class 333270bm have rank \(1\).
Complex multiplication
The elliptic curves in class 333270bm do not have complex multiplication.Modular form 333270.2.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 Cremona 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 Cremona labels.
