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SageMath
E = EllipticCurve("dt1")
E.isogeny_class()
Elliptic curves in class 152880.dt
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 152880.dt1 | 152880dg4 | \([0, -1, 0, -379080, -89692560]\) | \(12501706118329/2570490\) | \(1238694207528960\) | \([2]\) | \(1179648\) | \(1.8931\) | |
| 152880.dt2 | 152880dg2 | \([0, -1, 0, -26280, -1069200]\) | \(4165509529/1368900\) | \(659659637145600\) | \([2, 2]\) | \(589824\) | \(1.5466\) | |
| 152880.dt3 | 152880dg1 | \([0, -1, 0, -10600, 410992]\) | \(273359449/9360\) | \(4510493245440\) | \([2]\) | \(294912\) | \(1.2000\) | \(\Gamma_0(N)\)-optimal |
| 152880.dt4 | 152880dg3 | \([0, -1, 0, 75640, -7429008]\) | \(99317171591/106616250\) | \(-51377337123840000\) | \([2]\) | \(1179648\) | \(1.8931\) |
Rank
sage: E.rank()
The elliptic curves in class 152880.dt have rank \(1\).
Complex multiplication
The elliptic curves in class 152880.dt do not have complex multiplication.Modular form 152880.2.a.dt
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.
