Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 457776.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.bw1 | 457776bw2 | \([0, 0, 0, -6845307771, -217990506787670]\) | \(2418067440128989194388361/8359273562112\) | \(122631708372043409915904\) | \([2]\) | \(313786368\) | \(4.0741\) | |
457776.bw2 | 457776bw1 | \([0, 0, 0, -428022651, -3402909659990]\) | \(591139158854005457801/1097587482427392\) | \(16101761362124191159025664\) | \([2]\) | \(156893184\) | \(3.7275\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 457776.bw have rank \(0\).
Complex multiplication
The elliptic curves in class 457776.bw do not have complex multiplication.Modular form 457776.2.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.