Show commands:
SageMath
E = EllipticCurve("bw1")
E.isogeny_class()
Elliptic curves in class 35520bw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35520.b2 | 35520bw1 | \([0, -1, 0, 999, -999]\) | \(26892143936/15609375\) | \(-63936000000\) | \([2]\) | \(32256\) | \(0.76288\) | \(\Gamma_0(N)\)-optimal |
| 35520.b1 | 35520bw2 | \([0, -1, 0, -4001, -3999]\) | \(216216072008/124750125\) | \(4087812096000\) | \([2]\) | \(64512\) | \(1.1095\) |
Rank
sage: E.rank()
The elliptic curves in class 35520bw have rank \(1\).
Complex multiplication
The elliptic curves in class 35520bw do not have complex multiplication.Modular form 35520.2.a.bw
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.
