Show commands:
SageMath
E = EllipticCurve("y1")
E.isogeny_class()
Elliptic curves in class 24882.y
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.y1 | 24882w2 | \([1, 1, 1, -19813, 1065173]\) | \(860153182858140625/2279464902\) | \(2279464902\) | \([2]\) | \(33792\) | \(1.0308\) | |
24882.y2 | 24882w1 | \([1, 1, 1, -1223, 16697]\) | \(-202313692752625/10823819292\) | \(-10823819292\) | \([2]\) | \(16896\) | \(0.68427\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 24882.y have rank \(0\).
Complex multiplication
The elliptic curves in class 24882.y do not have complex multiplication.Modular form 24882.2.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.