Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 247962.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
247962.y1 | 247962y1 | \([1, 1, 1, -1668801895, 26266680670493]\) | \(-21293376668673906679951249/26211168887701209984\) | \(-632673897597541207372288896\) | \([]\) | \(173859840\) | \(4.0524\) | \(\Gamma_0(N)\)-optimal |
247962.y2 | 247962y2 | \([1, 1, 1, 4726042715, -1648527545143447]\) | \(483641001192506212470106511/48918776756543177755473774\) | \(-1180780349356657154552013347615406\) | \([]\) | \(1217018880\) | \(5.0254\) |
Rank
sage: E.rank()
The elliptic curves in class 247962.y have rank \(0\).
Complex multiplication
The elliptic curves in class 247962.y do not have complex multiplication.Modular form 247962.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.