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SageMath
E = EllipticCurve("jx1")
E.isogeny_class()
Elliptic curves in class 100800.jx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100800.jx1 | 100800np2 | \([0, 0, 0, -724800, -237508000]\) | \(-225637236736/1715\) | \(-320060160000000\) | \([]\) | \(829440\) | \(1.9581\) | |
100800.jx2 | 100800np1 | \([0, 0, 0, -4800, -628000]\) | \(-65536/875\) | \(-163296000000000\) | \([]\) | \(276480\) | \(1.4088\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.jx have rank \(0\).
Complex multiplication
The elliptic curves in class 100800.jx do not have complex multiplication.Modular form 100800.2.a.jx
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.