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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 4704.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4704.be1 | 4704bd2 | \([0, 1, 0, -10992, -447252]\) | \(2438569736/21\) | \(1264962048\) | \([2]\) | \(6144\) | \(0.91432\) | |
| 4704.be2 | 4704bd3 | \([0, 1, 0, -2417, 37407]\) | \(3241792/567\) | \(273231802368\) | \([4]\) | \(6144\) | \(0.91432\) | |
| 4704.be3 | 4704bd1 | \([0, 1, 0, -702, -6840]\) | \(5088448/441\) | \(3320525376\) | \([2, 2]\) | \(3072\) | \(0.56775\) | \(\Gamma_0(N)\)-optimal |
| 4704.be4 | 4704bd4 | \([0, 1, 0, 768, -30360]\) | \(830584/7203\) | \(-433881982464\) | \([2]\) | \(6144\) | \(0.91432\) |
Rank
sage: E.rank()
The elliptic curves in class 4704.be have rank \(0\).
Complex multiplication
The elliptic curves in class 4704.be do not have complex multiplication.Modular form 4704.2.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 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.
