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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 22800.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 22800.cw1 | 22800de4 | \([0, 1, 0, -40608, -3163212]\) | \(115714886617/1539\) | \(98496000000\) | \([2]\) | \(49152\) | \(1.2529\) | |
| 22800.cw2 | 22800de2 | \([0, 1, 0, -2608, -47212]\) | \(30664297/3249\) | \(207936000000\) | \([2, 2]\) | \(24576\) | \(0.90628\) | |
| 22800.cw3 | 22800de1 | \([0, 1, 0, -608, 4788]\) | \(389017/57\) | \(3648000000\) | \([2]\) | \(12288\) | \(0.55971\) | \(\Gamma_0(N)\)-optimal |
| 22800.cw4 | 22800de3 | \([0, 1, 0, 3392, -227212]\) | \(67419143/390963\) | \(-25021632000000\) | \([2]\) | \(49152\) | \(1.2529\) |
Rank
sage: E.rank()
The elliptic curves in class 22800.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 22800.cw do not have complex multiplication.Modular form 22800.2.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 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.
