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SageMath
E = EllipticCurve("rd1")
E.isogeny_class()
Elliptic curves in class 235200.rd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
235200.rd1 | 235200rd3 | \([0, 1, 0, -14192033, 20571636063]\) | \(2624033547076/324135\) | \(39049378421760000000\) | \([2]\) | \(14155776\) | \(2.7825\) | |
235200.rd2 | 235200rd2 | \([0, 1, 0, -962033, 263586063]\) | \(3269383504/893025\) | \(26896255545600000000\) | \([2, 2]\) | \(7077888\) | \(2.4360\) | |
235200.rd3 | 235200rd1 | \([0, 1, 0, -349533, -76351437]\) | \(2508888064/118125\) | \(222356610000000000\) | \([2]\) | \(3538944\) | \(2.0894\) | \(\Gamma_0(N)\)-optimal |
235200.rd4 | 235200rd4 | \([0, 1, 0, 2467967, 1721336063]\) | \(13799183324/18600435\) | \(-2240842319170560000000\) | \([2]\) | \(14155776\) | \(2.7825\) |
Rank
sage: E.rank()
The elliptic curves in class 235200.rd have rank \(0\).
Complex multiplication
The elliptic curves in class 235200.rd do not have complex multiplication.Modular form 235200.2.a.rd
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.