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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 41616.v
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 41616.v1 | 41616cl4 | \([0, 0, 0, -3774051, -2822017374]\) | \(82483294977/17\) | \(1225264712159232\) | \([2]\) | \(589824\) | \(2.2824\) | |
| 41616.v2 | 41616cl2 | \([0, 0, 0, -236691, -43774830]\) | \(20346417/289\) | \(20829500106706944\) | \([2, 2]\) | \(294912\) | \(1.9359\) | |
| 41616.v3 | 41616cl3 | \([0, 0, 0, -28611, -118059390]\) | \(-35937/83521\) | \(-6019725530838306816\) | \([2]\) | \(589824\) | \(2.2824\) | |
| 41616.v4 | 41616cl1 | \([0, 0, 0, -28611, 795906]\) | \(35937/17\) | \(1225264712159232\) | \([2]\) | \(147456\) | \(1.5893\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41616.v have rank \(1\).
Complex multiplication
The elliptic curves in class 41616.v do not have complex multiplication.Modular form 41616.2.a.v
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
