Show commands:
SageMath
E = EllipticCurve("ce1")
E.isogeny_class()
Elliptic curves in class 266175.ce
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
266175.ce1 | 266175ce2 | \([0, 0, 1, -69039750, 221645777031]\) | \(-756218111874334720/3363432789843\) | \(-161866516852127907421875\) | \([]\) | \(31104000\) | \(3.3058\) | |
266175.ce2 | 266175ce1 | \([0, 0, 1, 2037750, 1607606406]\) | \(19444740423680/34451725707\) | \(-1658002757354729296875\) | \([]\) | \(10368000\) | \(2.7565\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 266175.ce have rank \(1\).
Complex multiplication
The elliptic curves in class 266175.ce do not have complex multiplication.Modular form 266175.2.a.ce
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.