Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 26928.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
26928.bw1 | 26928bj1 | \([0, 0, 0, -130179, 17935490]\) | \(81706955619457/744505344\) | \(2223081045098496\) | \([2]\) | \(215040\) | \(1.7670\) | \(\Gamma_0(N)\)-optimal |
26928.bw2 | 26928bj2 | \([0, 0, 0, -38019, 42837122]\) | \(-2035346265217/264305213568\) | \(-789211138830630912\) | \([2]\) | \(430080\) | \(2.1136\) |
Rank
sage: E.rank()
The elliptic curves in class 26928.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 26928.bw do not have complex multiplication.Modular form 26928.2.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.