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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 40560.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 40560.be1 | 40560bu4 | \([0, -1, 0, -233973120, -1377439315968]\) | \(71647584155243142409/10140000\) | \(200473981992960000\) | \([2]\) | \(5160960\) | \(3.1729\) | |
| 40560.be2 | 40560bu3 | \([0, -1, 0, -16787840, -14729226240]\) | \(26465989780414729/10571870144160\) | \(209012318038682769162240\) | \([2]\) | \(5160960\) | \(3.1729\) | |
| 40560.be3 | 40560bu2 | \([0, -1, 0, -14624640, -21514752000]\) | \(17496824387403529/6580454400\) | \(130099595354151321600\) | \([2, 2]\) | \(2580480\) | \(2.8263\) | |
| 40560.be4 | 40560bu1 | \([0, -1, 0, -780160, -437915648]\) | \(-2656166199049/2658140160\) | \(-52553051535562506240\) | \([2]\) | \(1290240\) | \(2.4797\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 40560.be have rank \(1\).
Complex multiplication
The elliptic curves in class 40560.be do not have complex multiplication.Modular form 40560.2.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.
