Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 72128.bw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.bw1 | 72128q2 | \([0, -1, 0, -95713, -11364639]\) | \(12576878500/1127\) | \(8689445961728\) | \([2]\) | \(245760\) | \(1.5228\) | |
72128.bw2 | 72128q1 | \([0, -1, 0, -5553, -202831]\) | \(-9826000/3703\) | \(-7137759182848\) | \([2]\) | \(122880\) | \(1.1762\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 72128.bw have rank \(1\).
Complex multiplication
The elliptic curves in class 72128.bw do not have complex multiplication.Modular form 72128.2.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.