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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 92480cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 92480.cd3 | 92480cw1 | \([0, 0, 0, -165308, -25862032]\) | \(1263257424/425\) | \(168074720460800\) | \([2]\) | \(294912\) | \(1.7019\) | \(\Gamma_0(N)\)-optimal |
| 92480.cd2 | 92480cw2 | \([0, 0, 0, -188428, -18158448]\) | \(467720676/180625\) | \(285727024783360000\) | \([2, 2]\) | \(589824\) | \(2.0485\) | |
| 92480.cd4 | 92480cw3 | \([0, 0, 0, 597652, -130410672]\) | \(7462174302/6640625\) | \(-21009340057600000000\) | \([2]\) | \(1179648\) | \(2.3950\) | |
| 92480.cd1 | 92480cw4 | \([0, 0, 0, -1344428, 587123152]\) | \(84944038338/2088025\) | \(6606008812991283200\) | \([2]\) | \(1179648\) | \(2.3950\) |
Rank
sage: E.rank()
The elliptic curves in class 92480cw have rank \(2\).
Complex multiplication
The elliptic curves in class 92480cw do not have complex multiplication.Modular form 92480.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
