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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 20160be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.bj4 | 20160be1 | \([0, 0, 0, 1332, 29808]\) | \(1367631/2800\) | \(-535088332800\) | \([2]\) | \(24576\) | \(0.93487\) | \(\Gamma_0(N)\)-optimal |
| 20160.bj3 | 20160be2 | \([0, 0, 0, -10188, 320112]\) | \(611960049/122500\) | \(23410114560000\) | \([2, 2]\) | \(49152\) | \(1.2814\) | |
| 20160.bj2 | 20160be3 | \([0, 0, 0, -50508, -4082832]\) | \(74565301329/5468750\) | \(1045094400000000\) | \([2]\) | \(98304\) | \(1.6280\) | |
| 20160.bj1 | 20160be4 | \([0, 0, 0, -154188, 23302512]\) | \(2121328796049/120050\) | \(22941912268800\) | \([2]\) | \(98304\) | \(1.6280\) |
Rank
sage: E.rank()
The elliptic curves in class 20160be have rank \(0\).
Complex multiplication
The elliptic curves in class 20160be do not have complex multiplication.Modular form 20160.2.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.
