Show commands:
SageMath
E = EllipticCurve("eu1")
E.isogeny_class()
Elliptic curves in class 286110.eu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
286110.eu1 | 286110eu1 | \([1, -1, 1, -247583, 58404231]\) | \(-2575296504243/765952000\) | \(-499181919768576000\) | \([]\) | \(4147200\) | \(2.1103\) | \(\Gamma_0(N)\)-optimal |
286110.eu2 | 286110eu2 | \([1, -1, 1, 1833217, -488245049]\) | \(1434104310933/1046272480\) | \(-497083815261342444960\) | \([]\) | \(12441600\) | \(2.6596\) |
Rank
sage: E.rank()
The elliptic curves in class 286110.eu have rank \(1\).
Complex multiplication
The elliptic curves in class 286110.eu do not have complex multiplication.Modular form 286110.2.a.eu
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.