Show commands:
SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 414736.cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
414736.cb1 | 414736cb2 | \([0, -1, 0, -69269552, -209981665312]\) | \(1030541881826/62236321\) | \(2219878068772054402009088\) | \([2]\) | \(48660480\) | \(3.4241\) | \(\Gamma_0(N)\)-optimal* |
414736.cb2 | 414736cb1 | \([0, -1, 0, -68232712, -216915221760]\) | \(1969910093092/7889\) | \(140694515703641424896\) | \([2]\) | \(24330240\) | \(3.0775\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 414736.cb have rank \(1\).
Complex multiplication
The elliptic curves in class 414736.cb do not have complex multiplication.Modular form 414736.2.a.cb
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.