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SageMath
E = EllipticCurve("fe1")
E.isogeny_class()
Elliptic curves in class 257600fe
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 257600.fe2 | 257600fe1 | \([0, -1, 0, -263233, 52070337]\) | \(1969910093092/7889\) | \(8078336000000\) | \([2]\) | \(983040\) | \(1.6881\) | \(\Gamma_0(N)\)-optimal |
| 257600.fe1 | 257600fe2 | \([0, -1, 0, -267233, 50410337]\) | \(1030541881826/62236321\) | \(127459985408000000\) | \([2]\) | \(1966080\) | \(2.0347\) |
Rank
sage: E.rank()
The elliptic curves in class 257600fe have rank \(1\).
Complex multiplication
The elliptic curves in class 257600fe do not have complex multiplication.Modular form 257600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
