Show commands:
SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4998.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.j1 | 4998f2 | \([1, 1, 0, -13696, 606208]\) | \(5799070911693913/54760833024\) | \(2683280818176\) | \([]\) | \(12960\) | \(1.2056\) | |
4998.j2 | 4998f1 | \([1, 1, 0, -1201, -16043]\) | \(3914907891433/135834624\) | \(6655896576\) | \([]\) | \(4320\) | \(0.65630\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 4998.j have rank \(0\).
Complex multiplication
The elliptic curves in class 4998.j do not have complex multiplication.Modular form 4998.2.a.j
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.