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SageMath
E = EllipticCurve("ci1")
E.isogeny_class()
Elliptic curves in class 54208ci
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54208.g1 | 54208ci1 | \([0, 1, 0, -40817, -3249809]\) | \(-2141392/49\) | \(-172090739408896\) | \([]\) | \(253440\) | \(1.5192\) | \(\Gamma_0(N)\)-optimal |
| 54208.g2 | 54208ci2 | \([0, 1, 0, 172143, -14110769]\) | \(160630448/117649\) | \(-413189865320759296\) | \([]\) | \(760320\) | \(2.0685\) |
Rank
sage: E.rank()
The elliptic curves in class 54208ci have rank \(1\).
Complex multiplication
The elliptic curves in class 54208ci do not have complex multiplication.Modular form 54208.2.a.ci
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
