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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 39600cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 39600.j2 | 39600cw1 | \([0, 0, 0, 64125, -25818750]\) | \(185193/1936\) | \(-304850304000000000\) | \([2]\) | \(460800\) | \(2.0359\) | \(\Gamma_0(N)\)-optimal |
| 39600.j1 | 39600cw2 | \([0, 0, 0, -1015875, -366018750]\) | \(736314327/58564\) | \(9221721696000000000\) | \([2]\) | \(921600\) | \(2.3825\) |
Rank
sage: E.rank()
The elliptic curves in class 39600cw have rank \(0\).
Complex multiplication
The elliptic curves in class 39600cw do not have complex multiplication.Modular form 39600.2.a.cw
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.
