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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 16560z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.x4 | 16560z1 | \([0, 0, 0, -60963, -5793502]\) | \(226568219476347/3893440\) | \(430583316480\) | \([2]\) | \(41472\) | \(1.3615\) | \(\Gamma_0(N)\)-optimal |
| 16560.x3 | 16560z2 | \([0, 0, 0, -62883, -5409118]\) | \(248656466619387/29607177800\) | \(3274317007257600\) | \([2]\) | \(82944\) | \(1.7081\) | |
| 16560.x2 | 16560z3 | \([0, 0, 0, -99603, 2395602]\) | \(1355469437763/753664000\) | \(60761573425152000\) | \([2]\) | \(124416\) | \(1.9109\) | |
| 16560.x1 | 16560z4 | \([0, 0, 0, -1205523, 508685778]\) | \(2403250125069123/4232000000\) | \(341190475776000000\) | \([2]\) | \(248832\) | \(2.2574\) |
Rank
sage: E.rank()
The elliptic curves in class 16560z have rank \(0\).
Complex multiplication
The elliptic curves in class 16560z do not have complex multiplication.Modular form 16560.2.a.z
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 Cremona 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 Cremona labels.
