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SageMath
E = EllipticCurve("dw1")
E.isogeny_class()
Elliptic curves in class 44352.dw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 44352.dw1 | 44352dl4 | \([0, 0, 0, -23048364, -30199120432]\) | \(14171198121996897746/4077720290568771\) | \(389632241411638435381248\) | \([2]\) | \(5898240\) | \(3.2330\) | |
| 44352.dw2 | 44352dl2 | \([0, 0, 0, -21131724, -37384987120]\) | \(21843440425782779332/3100814593569\) | \(148143724213816590336\) | \([2, 2]\) | \(2949120\) | \(2.8864\) | |
| 44352.dw3 | 44352dl1 | \([0, 0, 0, -21131004, -37387662352]\) | \(87364831012240243408/1760913\) | \(21032232173568\) | \([2]\) | \(1474560\) | \(2.5399\) | \(\Gamma_0(N)\)-optimal |
| 44352.dw4 | 44352dl3 | \([0, 0, 0, -19226604, -44399638960]\) | \(-8226100326647904626/4152140742401883\) | \(-396743226321924614651904\) | \([2]\) | \(5898240\) | \(3.2330\) |
Rank
sage: E.rank()
The elliptic curves in class 44352.dw have rank \(1\).
Complex multiplication
The elliptic curves in class 44352.dw do not have complex multiplication.Modular form 44352.2.a.dw
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.
