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SageMath
E = EllipticCurve("bs1")
E.isogeny_class()
Elliptic curves in class 224400bs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 224400.fk2 | 224400bs1 | \([0, 1, 0, -218608, -38567212]\) | \(18052771191337/444958272\) | \(28477329408000000\) | \([2]\) | \(2064384\) | \(1.9411\) | \(\Gamma_0(N)\)-optimal |
| 224400.fk1 | 224400bs2 | \([0, 1, 0, -490608, 76216788]\) | \(204055591784617/78708537864\) | \(5037346423296000000\) | \([2]\) | \(4128768\) | \(2.2876\) |
Rank
sage: E.rank()
The elliptic curves in class 224400bs have rank \(2\).
Complex multiplication
The elliptic curves in class 224400bs do not have complex multiplication.Modular form 224400.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
