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SageMath
E = EllipticCurve("cd1")
E.isogeny_class()
Elliptic curves in class 154560.cd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 154560.cd1 | 154560gu3 | \([0, -1, 0, -117985, 14603617]\) | \(692895692874169/51420783750\) | \(13479649935360000\) | \([4]\) | \(1179648\) | \(1.8407\) | |
| 154560.cd2 | 154560gu2 | \([0, -1, 0, -23905, -1145375]\) | \(5763259856089/1143116100\) | \(299661026918400\) | \([2, 2]\) | \(589824\) | \(1.4942\) | |
| 154560.cd3 | 154560gu1 | \([0, -1, 0, -22625, -1302303]\) | \(4886171981209/270480\) | \(70904709120\) | \([2]\) | \(294912\) | \(1.1476\) | \(\Gamma_0(N)\)-optimal |
| 154560.cd4 | 154560gu4 | \([0, -1, 0, 49695, -6871455]\) | \(51774168853511/107398242630\) | \(-28153804915998720\) | \([2]\) | \(1179648\) | \(1.8407\) |
Rank
sage: E.rank()
The elliptic curves in class 154560.cd have rank \(1\).
Complex multiplication
The elliptic curves in class 154560.cd do not have complex multiplication.Modular form 154560.2.a.cd
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 LMFDB 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 LMFDB labels.
