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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 55488bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 55488.cn2 | 55488bs1 | \([0, 1, 0, -102657, -12763809]\) | \(-1579268174113/10077696\) | \(-763482379124736\) | \([]\) | \(435456\) | \(1.6930\) | \(\Gamma_0(N)\)-optimal |
| 55488.cn1 | 55488bs2 | \([0, 1, 0, -8327937, -9253043361]\) | \(-843137281012581793/216\) | \(-16364077056\) | \([]\) | \(1306368\) | \(2.2423\) |
Rank
sage: E.rank()
The elliptic curves in class 55488bs have rank \(0\).
Complex multiplication
The elliptic curves in class 55488bs do not have complex multiplication.Modular form 55488.2.a.bs
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
