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SageMath
E = EllipticCurve("ox1")
E.isogeny_class()
Elliptic curves in class 100800.ox
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 100800.ox1 | 100800fk4 | \([0, 0, 0, -75600300, 253007498000]\) | \(128025588102048008/7875\) | \(2939328000000000\) | \([2]\) | \(4718592\) | \(2.8766\) | |
| 100800.ox2 | 100800fk3 | \([0, 0, 0, -5292300, 2944622000]\) | \(43919722445768/15380859375\) | \(5740875000000000000000\) | \([2]\) | \(4718592\) | \(2.8766\) | |
| 100800.ox3 | 100800fk2 | \([0, 0, 0, -4725300, 3952748000]\) | \(250094631024064/62015625\) | \(2893401000000000000\) | \([2, 2]\) | \(2359296\) | \(2.5300\) | |
| 100800.ox4 | 100800fk1 | \([0, 0, 0, -260175, 77019500]\) | \(-2671731885376/1969120125\) | \(-1435488571125000000\) | \([2]\) | \(1179648\) | \(2.1834\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 100800.ox have rank \(1\).
Complex multiplication
The elliptic curves in class 100800.ox do not have complex multiplication.Modular form 100800.2.a.ox
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
