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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5808.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5808.f1 | 5808f4 | \([0, -1, 0, -85224, 9604608]\) | \(37736227588/33\) | \(59864589312\) | \([4]\) | \(23040\) | \(1.3683\) | |
5808.f2 | 5808f3 | \([0, -1, 0, -12624, -332880]\) | \(122657188/43923\) | \(79679768374272\) | \([2]\) | \(23040\) | \(1.3683\) | |
5808.f3 | 5808f2 | \([0, -1, 0, -5364, 149184]\) | \(37642192/1089\) | \(493882861824\) | \([2, 2]\) | \(11520\) | \(1.0217\) | |
5808.f4 | 5808f1 | \([0, -1, 0, 81, 7614]\) | \(2048/891\) | \(-25255373616\) | \([2]\) | \(5760\) | \(0.67512\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5808.f have rank \(0\).
Complex multiplication
The elliptic curves in class 5808.f do not have complex multiplication.Modular form 5808.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.