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SageMath
E = EllipticCurve("ck1")
E.isogeny_class()
Elliptic curves in class 173280.ck
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 173280.ck1 | 173280d2 | \([0, 1, 0, -57880, 5340380]\) | \(890277128/15\) | \(361312366080\) | \([2]\) | \(442368\) | \(1.3480\) | |
| 173280.ck2 | 173280d4 | \([0, 1, 0, -14560, -598792]\) | \(14172488/1875\) | \(45164045760000\) | \([2]\) | \(442368\) | \(1.3480\) | |
| 173280.ck3 | 173280d1 | \([0, 1, 0, -3730, 77000]\) | \(1906624/225\) | \(677460686400\) | \([2, 2]\) | \(221184\) | \(1.0014\) | \(\Gamma_0(N)\)-optimal |
| 173280.ck4 | 173280d3 | \([0, 1, 0, 5295, 400095]\) | \(85184/405\) | \(-78043471073280\) | \([2]\) | \(442368\) | \(1.3480\) |
Rank
sage: E.rank()
The elliptic curves in class 173280.ck have rank \(1\).
Complex multiplication
The elliptic curves in class 173280.ck do not have complex multiplication.Modular form 173280.2.a.ck
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.
