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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 4560.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4560.k1 | 4560u3 | \([0, -1, 0, -48640, -4112768]\) | \(3107086841064961/570\) | \(2334720\) | \([2]\) | \(9216\) | \(1.0577\) | |
| 4560.k2 | 4560u4 | \([0, -1, 0, -3520, -41600]\) | \(1177918188481/488703750\) | \(2001730560000\) | \([4]\) | \(9216\) | \(1.0577\) | |
| 4560.k3 | 4560u2 | \([0, -1, 0, -3040, -63488]\) | \(758800078561/324900\) | \(1330790400\) | \([2, 2]\) | \(4608\) | \(0.71109\) | |
| 4560.k4 | 4560u1 | \([0, -1, 0, -160, -1280]\) | \(-111284641/123120\) | \(-504299520\) | \([2]\) | \(2304\) | \(0.36452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4560.k have rank \(0\).
Complex multiplication
The elliptic curves in class 4560.k do not have complex multiplication.Modular form 4560.2.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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
