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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 283920.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 283920.w1 | 283920w4 | \([0, -1, 0, -1629216, -712825920]\) | \(24190225473961/2879296875\) | \(56925454622400000000\) | \([2]\) | \(8257536\) | \(2.5217\) | |
| 283920.w2 | 283920w2 | \([0, -1, 0, -398896, 85405696]\) | \(355045312441/46580625\) | \(920927354780160000\) | \([2, 2]\) | \(4128768\) | \(2.1752\) | |
| 283920.w3 | 283920w1 | \([0, -1, 0, -385376, 92208960]\) | \(320153881321/6825\) | \(134934410956800\) | \([2]\) | \(2064384\) | \(1.8286\) | \(\Gamma_0(N)\)-optimal |
| 283920.w4 | 283920w3 | \([0, -1, 0, 615104, 448012096]\) | \(1301812981559/5143122075\) | \(-101682658999126732800\) | \([2]\) | \(8257536\) | \(2.5217\) |
Rank
sage: E.rank()
The elliptic curves in class 283920.w have rank \(0\).
Complex multiplication
The elliptic curves in class 283920.w do not have complex multiplication.Modular form 283920.2.a.w
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
