Show commands:
SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 4998.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.x1 | 4998x1 | \([1, 0, 1, -124, -346]\) | \(1771561/612\) | \(72001188\) | \([2]\) | \(2880\) | \(0.20943\) | \(\Gamma_0(N)\)-optimal |
4998.x2 | 4998x2 | \([1, 0, 1, 366, -2306]\) | \(46268279/46818\) | \(-5508090882\) | \([2]\) | \(5760\) | \(0.55600\) |
Rank
sage: E.rank()
The elliptic curves in class 4998.x have rank \(0\).
Complex multiplication
The elliptic curves in class 4998.x do not have complex multiplication.Modular form 4998.2.a.x
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.