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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 28560.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.dd1 | 28560dw4 | \([0, 1, 0, -16240, -620140]\) | \(115650783909361/27072079335\) | \(110887236956160\) | \([2]\) | \(98304\) | \(1.4068\) | |
| 28560.dd2 | 28560dw2 | \([0, 1, 0, -5440, 144500]\) | \(4347507044161/258084225\) | \(1057112985600\) | \([2, 2]\) | \(49152\) | \(1.0602\) | |
| 28560.dd3 | 28560dw1 | \([0, 1, 0, -5360, 149268]\) | \(4158523459441/16065\) | \(65802240\) | \([2]\) | \(24576\) | \(0.71365\) | \(\Gamma_0(N)\)-optimal |
| 28560.dd4 | 28560dw3 | \([0, 1, 0, 4080, 605268]\) | \(1833318007919/39525924375\) | \(-161898186240000\) | \([4]\) | \(98304\) | \(1.4068\) |
Rank
sage: E.rank()
The elliptic curves in class 28560.dd have rank \(1\).
Complex multiplication
The elliptic curves in class 28560.dd do not have complex multiplication.Modular form 28560.2.a.dd
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.
