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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 17600cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17600.ck2 | 17600cf1 | \([0, 1, 0, 15967, 3140063]\) | \(109902239/1100000\) | \(-4505600000000000\) | \([]\) | \(92160\) | \(1.6848\) | \(\Gamma_0(N)\)-optimal |
| 17600.ck1 | 17600cf2 | \([0, 1, 0, -9504033, 11274260063]\) | \(-23178622194826561/1610510\) | \(-6596648960000000\) | \([]\) | \(460800\) | \(2.4895\) |
Rank
sage: E.rank()
The elliptic curves in class 17600cf have rank \(1\).
Complex multiplication
The elliptic curves in class 17600cf do not have complex multiplication.Modular form 17600.2.a.cf
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.
