Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 106560.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
106560.z1 | 106560bw1 | \([0, 0, 0, -2028, 33968]\) | \(4826809/185\) | \(35354050560\) | \([2]\) | \(73728\) | \(0.79196\) | \(\Gamma_0(N)\)-optimal |
106560.z2 | 106560bw2 | \([0, 0, 0, 852, 122672]\) | \(357911/34225\) | \(-6540499353600\) | \([2]\) | \(147456\) | \(1.1385\) |
Rank
sage: E.rank()
The elliptic curves in class 106560.z have rank \(1\).
Complex multiplication
The elliptic curves in class 106560.z do not have complex multiplication.Modular form 106560.2.a.z
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.