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SageMath
E = EllipticCurve("lw1")
E.isogeny_class()
Elliptic curves in class 235200.lw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 235200.lw1 | 235200lw2 | \([0, -1, 0, -10033, 369937]\) | \(1272112/75\) | \(6585600000000\) | \([2]\) | \(589824\) | \(1.2129\) | |
| 235200.lw2 | 235200lw1 | \([0, -1, 0, 467, 23437]\) | \(2048/45\) | \(-246960000000\) | \([2]\) | \(294912\) | \(0.86632\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 235200.lw have rank \(1\).
Complex multiplication
The elliptic curves in class 235200.lw do not have complex multiplication.Modular form 235200.2.a.lw
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.
