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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 106560.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 106560.k1 | 106560ds2 | \([0, 0, 0, -56268, -5127408]\) | \(15273442188/34225\) | \(44148370636800\) | \([2]\) | \(442368\) | \(1.5005\) | |
| 106560.k2 | 106560ds1 | \([0, 0, 0, -2268, -137808]\) | \(-4000752/23125\) | \(-7457495040000\) | \([2]\) | \(221184\) | \(1.1539\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 106560.k have rank \(1\).
Complex multiplication
The elliptic curves in class 106560.k do not have complex multiplication.Modular form 106560.2.a.k
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.
