Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 455175.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
455175.bw1 | 455175bw2 | \([1, -1, 1, -13656605, 9493161522]\) | \(208527857/91875\) | \(124103834072734482421875\) | \([2]\) | \(40108032\) | \(3.1271\) | \(\Gamma_0(N)\)-optimal* |
455175.bw2 | 455175bw1 | \([1, -1, 1, 2924770, 1102985772]\) | \(2048383/1575\) | \(-2127494298389733984375\) | \([2]\) | \(20054016\) | \(2.7805\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 455175.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 455175.bw do not have complex multiplication.Modular form 455175.2.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.