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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 38720.bx
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.bx1 | 38720db1 | \([0, 0, 0, -18392, -926376]\) | \(379275264/15125\) | \(27437936768000\) | \([2]\) | \(92160\) | \(1.3451\) | \(\Gamma_0(N)\)-optimal |
| 38720.bx2 | 38720db2 | \([0, 0, 0, 8228, -3386064]\) | \(2122416/171875\) | \(-4988715776000000\) | \([2]\) | \(184320\) | \(1.6917\) |
Rank
sage: E.rank()
The elliptic curves in class 38720.bx have rank \(0\).
Complex multiplication
The elliptic curves in class 38720.bx do not have complex multiplication.Modular form 38720.2.a.bx
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.
