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SageMath
E = EllipticCurve("fb1")
E.isogeny_class()
Elliptic curves in class 267696fb
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 267696.fb3 | 267696fb1 | \([0, 0, 0, -18759, -953498]\) | \(810448/33\) | \(29726347292928\) | \([2]\) | \(589824\) | \(1.3510\) | \(\Gamma_0(N)\)-optimal |
| 267696.fb2 | 267696fb2 | \([0, 0, 0, -49179, 2922010]\) | \(3650692/1089\) | \(3923877842666496\) | \([2, 2]\) | \(1179648\) | \(1.6976\) | |
| 267696.fb1 | 267696fb3 | \([0, 0, 0, -718419, 234345202]\) | \(5690357426/891\) | \(6420891015272448\) | \([2]\) | \(2359296\) | \(2.0442\) | |
| 267696.fb4 | 267696fb4 | \([0, 0, 0, 133341, 19531330]\) | \(36382894/43923\) | \(-316526145975097344\) | \([2]\) | \(2359296\) | \(2.0442\) |
Rank
sage: E.rank()
The elliptic curves in class 267696fb have rank \(0\).
Complex multiplication
The elliptic curves in class 267696fb do not have complex multiplication.Modular form 267696.2.a.fb
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
