Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 435344.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
435344.bw1 | 435344bw2 | \([0, -1, 0, -470552, -123929872]\) | \(582810602977/829472\) | \(16399167139217408\) | \([2]\) | \(4147200\) | \(2.0143\) | |
435344.bw2 | 435344bw1 | \([0, -1, 0, -37912, -714000]\) | \(304821217/164864\) | \(3259461791645696\) | \([2]\) | \(2073600\) | \(1.6677\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 435344.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 435344.bw do not have complex multiplication.Modular form 435344.2.a.bw
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.