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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 18648.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18648.m1 | 18648u1 | \([0, 0, 0, -90, -243]\) | \(6912000/1813\) | \(21146832\) | \([2]\) | \(3584\) | \(0.11439\) | \(\Gamma_0(N)\)-optimal |
| 18648.m2 | 18648u2 | \([0, 0, 0, 225, -1566]\) | \(6750000/9583\) | \(-1788417792\) | \([2]\) | \(7168\) | \(0.46097\) |
Rank
sage: E.rank()
The elliptic curves in class 18648.m have rank \(1\).
Complex multiplication
The elliptic curves in class 18648.m do not have complex multiplication.Modular form 18648.2.a.m
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.
