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SageMath
E = EllipticCurve("fu1")
E.isogeny_class()
Elliptic curves in class 25200.fu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25200.fu1 | 25200do2 | \([0, 0, 0, -64875, 6356250]\) | \(139798359/98\) | \(21168000000000\) | \([2]\) | \(92160\) | \(1.4933\) | |
25200.fu2 | 25200do1 | \([0, 0, 0, -4875, 56250]\) | \(59319/28\) | \(6048000000000\) | \([2]\) | \(46080\) | \(1.1467\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25200.fu have rank \(0\).
Complex multiplication
The elliptic curves in class 25200.fu do not have complex multiplication.Modular form 25200.2.a.fu
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.