Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 160446.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160446.bw1 | 160446q1 | \([1, 0, 0, -11316, 329088]\) | \(90458382169/25788048\) | \(45685100102928\) | \([2]\) | \(768000\) | \(1.3277\) | \(\Gamma_0(N)\)-optimal |
160446.bw2 | 160446q2 | \([1, 0, 0, 29824, 2180388]\) | \(1656015369191/2114999172\) | \(-3746850048147492\) | \([2]\) | \(1536000\) | \(1.6743\) |
Rank
sage: E.rank()
The elliptic curves in class 160446.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 160446.bw do not have complex multiplication.Modular form 160446.2.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.