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SageMath
E = EllipticCurve("dl1")
E.isogeny_class()
Elliptic curves in class 142800dl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 142800.cs3 | 142800dl1 | \([0, -1, 0, -134008, 18926512]\) | \(4158523459441/16065\) | \(1028160000000\) | \([2]\) | \(589824\) | \(1.5184\) | \(\Gamma_0(N)\)-optimal |
| 142800.cs2 | 142800dl2 | \([0, -1, 0, -136008, 18334512]\) | \(4347507044161/258084225\) | \(16517390400000000\) | \([2, 2]\) | \(1179648\) | \(1.8649\) | |
| 142800.cs4 | 142800dl3 | \([0, -1, 0, 101992, 75454512]\) | \(1833318007919/39525924375\) | \(-2529659160000000000\) | \([2]\) | \(2359296\) | \(2.2115\) | |
| 142800.cs1 | 142800dl4 | \([0, -1, 0, -406008, -76705488]\) | \(115650783909361/27072079335\) | \(1732613077440000000\) | \([2]\) | \(2359296\) | \(2.2115\) |
Rank
sage: E.rank()
The elliptic curves in class 142800dl have rank \(1\).
Complex multiplication
The elliptic curves in class 142800dl do not have complex multiplication.Modular form 142800.2.a.dl
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.
