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SageMath
E = EllipticCurve("os1")
E.isogeny_class()
Elliptic curves in class 235200.os
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.os1 | 235200os2 | \([0, 1, 0, -6714633, 6694747863]\) | \(4446542056384/25725\) | \(193697313600000000\) | \([2]\) | \(8847360\) | \(2.5074\) | |
| 235200.os2 | 235200os1 | \([0, 1, 0, -412008, 108504738]\) | \(-65743598656/5294205\) | \(-622857924045000000\) | \([2]\) | \(4423680\) | \(2.1609\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.os have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.os do not have complex multiplication.Modular form 235200.2.a.os
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
