Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 44100bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
44100.bc1 | 44100bw1 | \([0, 0, 0, -44776200, 76676749625]\) | \(463030539649024/149501953125\) | \(3205550650363769531250000\) | \([2]\) | \(7741440\) | \(3.4057\) | \(\Gamma_0(N)\)-optimal |
44100.bc2 | 44100bw2 | \([0, 0, 0, 127489425, 524050577750]\) | \(667990736021936/732392128125\) | \(-251257727520865012500000000\) | \([2]\) | \(15482880\) | \(3.7523\) |
Rank
sage: E.rank()
The elliptic curves in class 44100bw have rank \(0\).
Complex multiplication
The elliptic curves in class 44100bw do not have complex multiplication.Modular form 44100.2.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 Cremona 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 Cremona labels.