Show commands:
SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 25886.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 25886.b1 | 25886b2 | \([1, -1, 1, -6137178, 5605249769]\) | \(4044073786633161/194342971312\) | \(1228512477684543850288\) | \([2]\) | \(1774080\) | \(2.8068\) | |
| 25886.b2 | 25886b1 | \([1, -1, 1, 223382, 338706089]\) | \(195011097399/7955492608\) | \(-50289557008803841792\) | \([2]\) | \(887040\) | \(2.4602\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 25886.b have rank \(0\).
Complex multiplication
The elliptic curves in class 25886.b do not have complex multiplication.Modular form 25886.2.a.b
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.
