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SageMath
E = EllipticCurve("nd1")
E.isogeny_class()
Elliptic curves in class 235200nd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.nd3 | 235200nd1 | \([0, -1, 0, -349533, 76351437]\) | \(2508888064/118125\) | \(222356610000000000\) | \([2]\) | \(3538944\) | \(2.0894\) | \(\Gamma_0(N)\)-optimal |
| 235200.nd2 | 235200nd2 | \([0, -1, 0, -962033, -263586063]\) | \(3269383504/893025\) | \(26896255545600000000\) | \([2, 2]\) | \(7077888\) | \(2.4360\) | |
| 235200.nd4 | 235200nd3 | \([0, -1, 0, 2467967, -1721336063]\) | \(13799183324/18600435\) | \(-2240842319170560000000\) | \([2]\) | \(14155776\) | \(2.7825\) | |
| 235200.nd1 | 235200nd4 | \([0, -1, 0, -14192033, -20571636063]\) | \(2624033547076/324135\) | \(39049378421760000000\) | \([2]\) | \(14155776\) | \(2.7825\) |
Rank
sage: E.rank()
The elliptic curves in class 235200nd have rank \(0\).
Complex multiplication
The elliptic curves in class 235200nd do not have complex multiplication.Modular form 235200.2.a.nd
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.
