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SageMath
E = EllipticCurve("bm1")
E.isogeny_class()
Elliptic curves in class 17600bm
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.bn1 | 17600bm1 | \([0, 0, 0, -3800, 87000]\) | \(379275264/15125\) | \(242000000000\) | \([2]\) | \(18432\) | \(0.95087\) | \(\Gamma_0(N)\)-optimal |
| 17600.bn2 | 17600bm2 | \([0, 0, 0, 1700, 318000]\) | \(2122416/171875\) | \(-44000000000000\) | \([2]\) | \(36864\) | \(1.2974\) |
Rank
sage: E.rank()
The elliptic curves in class 17600bm have rank \(2\).
Complex multiplication
The elliptic curves in class 17600bm do not have complex multiplication.Modular form 17600.2.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.
