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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 86640bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 86640.k1 | 86640bm1 | \([0, -1, 0, -208056, -41990544]\) | \(-14317849/2700\) | \(-187824620383027200\) | \([]\) | \(1181952\) | \(2.0386\) | \(\Gamma_0(N)\)-optimal |
| 86640.k2 | 86640bm2 | \([0, -1, 0, 1438104, 205591920]\) | \(4728305591/3000000\) | \(-208694022647808000000\) | \([]\) | \(3545856\) | \(2.5879\) |
Rank
sage: E.rank()
The elliptic curves in class 86640bm have rank \(0\).
Complex multiplication
The elliptic curves in class 86640bm do not have complex multiplication.Modular form 86640.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
