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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 29040.g
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29040.g1 | 29040f1 | \([0, -1, 0, -1080691, 428978266]\) | \(4924392082991104/49825153125\) | \(1412292769524450000\) | \([2]\) | \(460800\) | \(2.3006\) | \(\Gamma_0(N)\)-optimal |
| 29040.g2 | 29040f2 | \([0, -1, 0, -275436, 1052889840]\) | \(-5095552972624/1052841796875\) | \(-477484407427500000000\) | \([2]\) | \(921600\) | \(2.6472\) |
Rank
sage: E.rank()
The elliptic curves in class 29040.g have rank \(0\).
Complex multiplication
The elliptic curves in class 29040.g do not have complex multiplication.Modular form 29040.2.a.g
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.
