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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 4410be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4410.bc3 | 4410be1 | \([1, -1, 1, -1553, -14479]\) | \(4826809/1680\) | \(144087083280\) | \([2]\) | \(6144\) | \(0.84270\) | \(\Gamma_0(N)\)-optimal |
| 4410.bc2 | 4410be2 | \([1, -1, 1, -10373, 398297]\) | \(1439069689/44100\) | \(3782285936100\) | \([2, 2]\) | \(12288\) | \(1.1893\) | |
| 4410.bc1 | 4410be3 | \([1, -1, 1, -164723, 25773437]\) | \(5763259856089/5670\) | \(486293906070\) | \([2]\) | \(24576\) | \(1.5358\) | |
| 4410.bc4 | 4410be4 | \([1, -1, 1, 2857, 1334981]\) | \(30080231/9003750\) | \(-772216711953750\) | \([2]\) | \(24576\) | \(1.5358\) |
Rank
sage: E.rank()
The elliptic curves in class 4410be have rank \(0\).
Complex multiplication
The elliptic curves in class 4410be do not have complex multiplication.Modular form 4410.2.a.be
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 Cremona 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 Cremona labels.
