Show commands for:
SageMath
sage: E = EllipticCurve("bj1")
sage: E.isogeny_class()
Elliptic curves in class 54208.bj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
54208.bj1 | 54208bx4 | [0, 0, 0, -144716, 21189520] | [2] | 163840 | |
54208.bj2 | 54208bx3 | [0, 0, 0, -28556, -1469424] | [2] | 163840 | |
54208.bj3 | 54208bx2 | [0, 0, 0, -9196, 319440] | [2, 2] | 81920 | |
54208.bj4 | 54208bx1 | [0, 0, 0, 484, 21296] | [2] | 40960 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54208.bj have rank \(1\).
Complex multiplication
The elliptic curves in class 54208.bj do not have complex multiplication.Modular form 54208.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.