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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 16560.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.cf1 | 16560bg4 | \([0, 0, 0, -565947, 146046186]\) | \(248656466619387/29607177800\) | \(2386977098290790400\) | \([2]\) | \(248832\) | \(2.2574\) | |
| 16560.cf2 | 16560bg3 | \([0, 0, 0, -548667, 156424554]\) | \(226568219476347/3893440\) | \(313895237713920\) | \([2]\) | \(124416\) | \(1.9109\) | |
| 16560.cf3 | 16560bg2 | \([0, 0, 0, -133947, -18840214]\) | \(2403250125069123/4232000000\) | \(468025344000000\) | \([2]\) | \(82944\) | \(1.7081\) | |
| 16560.cf4 | 16560bg1 | \([0, 0, 0, -11067, -88726]\) | \(1355469437763/753664000\) | \(83349209088000\) | \([2]\) | \(41472\) | \(1.3615\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 16560.cf do not have complex multiplication.Modular form 16560.2.a.cf
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
