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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 212160.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 212160.k1 | 212160dj2 | \([0, -1, 0, -172721, 27685521]\) | \(34780972302198736/1711783125\) | \(28045854720000\) | \([2]\) | \(983040\) | \(1.6522\) | |
| 212160.k2 | 212160dj1 | \([0, -1, 0, -10221, 483021]\) | \(-115331093579776/30301171875\) | \(-31028400000000\) | \([2]\) | \(491520\) | \(1.3057\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212160.k have rank \(1\).
Complex multiplication
The elliptic curves in class 212160.k do not have complex multiplication.Modular form 212160.2.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.
