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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 1104.a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1104.a1 | 1104a3 | \([0, -1, 0, -2944, -60512]\) | \(1378334691074/69\) | \(141312\) | \([2]\) | \(512\) | \(0.46266\) | |
| 1104.a2 | 1104a4 | \([0, -1, 0, -304, 544]\) | \(1522096994/839523\) | \(1719343104\) | \([4]\) | \(512\) | \(0.46266\) | |
| 1104.a3 | 1104a2 | \([0, -1, 0, -184, -896]\) | \(676449508/4761\) | \(4875264\) | \([2, 2]\) | \(256\) | \(0.11608\) | |
| 1104.a4 | 1104a1 | \([0, -1, 0, -4, -32]\) | \(-35152/1863\) | \(-476928\) | \([2]\) | \(128\) | \(-0.23049\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1104.a have rank \(0\).
Complex multiplication
The elliptic curves in class 1104.a do not have complex multiplication.Modular form 1104.2.a.a
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.
