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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 162450.db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 162450.db1 | 162450b4 | \([1, -1, 1, -2690240, 1693521987]\) | \(502270291349/1889568\) | \(8100683654424804000\) | \([2]\) | \(4608000\) | \(2.4875\) | |
| 162450.db2 | 162450b2 | \([1, -1, 1, -172265, -27473313]\) | \(131872229/18\) | \(77167006310250\) | \([2]\) | \(921600\) | \(1.6828\) | |
| 162450.db3 | 162450b3 | \([1, -1, 1, -91040, 50827587]\) | \(-19465109/248832\) | \(-1066756695232896000\) | \([2]\) | \(2304000\) | \(2.1410\) | |
| 162450.db4 | 162450b1 | \([1, -1, 1, -9815, -506613]\) | \(-24389/12\) | \(-51444670873500\) | \([2]\) | \(460800\) | \(1.3363\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 162450.db have rank \(1\).
Complex multiplication
The elliptic curves in class 162450.db do not have complex multiplication.Modular form 162450.2.a.db
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
