Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 194208.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
194208.bw1 | 194208bq2 | \([0, 1, 0, -9633, 340335]\) | \(1000000/63\) | \(6228651405312\) | \([2]\) | \(315392\) | \(1.2061\) | |
194208.bw2 | 194208bq1 | \([0, 1, 0, 482, 22724]\) | \(8000/147\) | \(-227086249152\) | \([2]\) | \(157696\) | \(0.85949\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 194208.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 194208.bw do not have complex multiplication.Modular form 194208.2.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.