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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 2496.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2496.k1 | 2496s3 | \([0, -1, 0, -1217, 16353]\) | \(3044193988/85293\) | \(5589762048\) | \([2]\) | \(2048\) | \(0.64941\) | |
| 2496.k2 | 2496s2 | \([0, -1, 0, -177, -495]\) | \(37642192/13689\) | \(224280576\) | \([2, 2]\) | \(1024\) | \(0.30283\) | |
| 2496.k3 | 2496s1 | \([0, -1, 0, -157, -707]\) | \(420616192/117\) | \(119808\) | \([2]\) | \(512\) | \(-0.043740\) | \(\Gamma_0(N)\)-optimal |
| 2496.k4 | 2496s4 | \([0, -1, 0, 543, -4095]\) | \(269676572/257049\) | \(-16845963264\) | \([2]\) | \(2048\) | \(0.64941\) |
Rank
sage: E.rank()
The elliptic curves in class 2496.k have rank \(0\).
Complex multiplication
The elliptic curves in class 2496.k do not have complex multiplication.Modular form 2496.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
