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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 56640cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 56640.ch2 | 56640cq1 | \([0, 1, 0, -1121, -14595]\) | \(2436396322816/44803125\) | \(2867400000\) | \([]\) | \(32000\) | \(0.60940\) | \(\Gamma_0(N)\)-optimal |
| 56640.ch1 | 56640cq2 | \([0, 1, 0, -77321, 8249685]\) | \(798806778238038016/10723864485\) | \(686327327040\) | \([]\) | \(160000\) | \(1.4141\) |
Rank
sage: E.rank()
The elliptic curves in class 56640cq have rank \(1\).
Complex multiplication
The elliptic curves in class 56640cq do not have complex multiplication.Modular form 56640.2.a.cq
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.
