Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 16560.bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 16560.bw1 | 16560ce2 | \([0, 0, 0, -16707, 797506]\) | \(172715635009/7935000\) | \(23693783040000\) | \([2]\) | \(36864\) | \(1.3280\) | |
| 16560.bw2 | 16560ce1 | \([0, 0, 0, 573, 47554]\) | \(6967871/331200\) | \(-988957900800\) | \([2]\) | \(18432\) | \(0.98141\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 16560.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 16560.bw do not have complex multiplication.Modular form 16560.2.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.
