Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 212268.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
212268.y1 | 212268cf2 | \([0, -1, 0, -784212, 247898232]\) | \(109744/9\) | \(4374077167509735168\) | \([2]\) | \(4064256\) | \(2.3194\) | |
212268.y2 | 212268cf1 | \([0, -1, 0, -165097, -21292970]\) | \(16384/3\) | \(91126607656452816\) | \([2]\) | \(2032128\) | \(1.9728\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 212268.y have rank \(0\).
Complex multiplication
The elliptic curves in class 212268.y do not have complex multiplication.Modular form 212268.2.a.y
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.