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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 202800f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
202800.ge1 | 202800f1 | \([0, 1, 0, -24650341408, 1489635885670388]\) | \(-134057911417971280740025/1872\) | \(-23131613306880000\) | \([]\) | \(135475200\) | \(4.1196\) | \(\Gamma_0(N)\)-optimal |
202800.ge2 | 202800f2 | \([0, 1, 0, -24018484208, 1569616224165588]\) | \(-198417696411528597145/22989483914821632\) | \(-177545356584666058771660800000000\) | \([]\) | \(677376000\) | \(4.9244\) |
Rank
sage: E.rank()
The elliptic curves in class 202800f have rank \(0\).
Complex multiplication
The elliptic curves in class 202800f do not have complex multiplication.Modular form 202800.2.a.f
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.