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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 44100cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44100.ds2 | 44100cl1 | \([0, 0, 0, -6894300, 6779523625]\) | \(4927700992/151875\) | \(1116956315504531250000\) | \([2]\) | \(2580480\) | \(2.8144\) | \(\Gamma_0(N)\)-optimal |
| 44100.ds1 | 44100cl2 | \([0, 0, 0, -16541175, -16382623250]\) | \(4253563312/1476225\) | \(173709046187264700000000\) | \([2]\) | \(5160960\) | \(3.1609\) |
Rank
sage: E.rank()
The elliptic curves in class 44100cl have rank \(0\).
Complex multiplication
The elliptic curves in class 44100cl do not have complex multiplication.Modular form 44100.2.a.cl
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 Cremona 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 Cremona labels.
