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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 122304fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122304.bw2 | 122304fe1 | \([0, -1, 0, 2239039, -14571166623]\) | \(40251338884511/2997011332224\) | \(-92430764926519574790144\) | \([]\) | \(10838016\) | \(3.0863\) | \(\Gamma_0(N)\)-optimal |
| 122304.bw1 | 122304fe2 | \([0, -1, 0, -11523219521, -476107872887583]\) | \(-5486773802537974663600129/2635437714\) | \(-81279480395041603584\) | \([]\) | \(75866112\) | \(4.0592\) |
Rank
sage: E.rank()
The elliptic curves in class 122304fe have rank \(1\).
Complex multiplication
The elliptic curves in class 122304fe do not have complex multiplication.Modular form 122304.2.a.fe
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
