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SageMath
E = EllipticCurve("el1")
E.isogeny_class()
Elliptic curves in class 436800.el
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
436800.el1 | 436800el4 | \([0, -1, 0, -135201633, -605046388863]\) | \(266912903848829942596/152163375\) | \(155815296000000000\) | \([2]\) | \(33030144\) | \(3.0599\) | |
436800.el2 | 436800el2 | \([0, -1, 0, -8451633, -9448138863]\) | \(260798860029250384/196803140625\) | \(50381604000000000000\) | \([2, 2]\) | \(16515072\) | \(2.7133\) | |
436800.el3 | 436800el3 | \([0, -1, 0, -6701633, -13474888863]\) | \(-32506165579682596/57814914850875\) | \(-59202472807296000000000\) | \([2]\) | \(33030144\) | \(3.0599\) | |
436800.el4 | 436800el1 | \([0, -1, 0, -639133, -80951363]\) | \(1804588288006144/866455078125\) | \(13863281250000000000\) | \([2]\) | \(8257536\) | \(2.3667\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 436800.el have rank \(0\).
Complex multiplication
The elliptic curves in class 436800.el do not have complex multiplication.Modular form 436800.2.a.el
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.