Show commands:
SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 82800cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 82800.dh2 | 82800cw1 | \([0, 0, 0, 482325, -132875750]\) | \(265971760991/317400000\) | \(-14808614400000000000\) | \([2]\) | \(1105920\) | \(2.3647\) | \(\Gamma_0(N)\)-optimal |
| 82800.dh1 | 82800cw2 | \([0, 0, 0, -2829675, -1268891750]\) | \(53706380371489/16171875000\) | \(754515000000000000000\) | \([2]\) | \(2211840\) | \(2.7113\) |
Rank
sage: E.rank()
The elliptic curves in class 82800cw have rank \(1\).
Complex multiplication
The elliptic curves in class 82800cw do not have complex multiplication.Modular form 82800.2.a.cw
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 Cremona 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 Cremona labels.
