Show commands:
SageMath
E = EllipticCurve("lk1")
E.isogeny_class()
Elliptic curves in class 221760.lk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
221760.lk1 | 221760ip1 | \([0, 0, 0, -4332, -107984]\) | \(188183524/3465\) | \(165542952960\) | \([2]\) | \(294912\) | \(0.94733\) | \(\Gamma_0(N)\)-optimal |
221760.lk2 | 221760ip2 | \([0, 0, 0, -12, -313616]\) | \(-2/444675\) | \(-42489357926400\) | \([2]\) | \(589824\) | \(1.2939\) |
Rank
sage: E.rank()
The elliptic curves in class 221760.lk have rank \(2\).
Complex multiplication
The elliptic curves in class 221760.lk do not have complex multiplication.Modular form 221760.2.a.lk
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.