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SageMath
E = EllipticCurve("be1")
E.isogeny_class()
Elliptic curves in class 33600.be
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 33600.be1 | 33600b4 | \([0, -1, 0, -373633, -87780863]\) | \(5633270409316/14175\) | \(14515200000000\) | \([2]\) | \(196608\) | \(1.7638\) | |
| 33600.be2 | 33600b3 | \([0, -1, 0, -65633, 4759137]\) | \(30534944836/8203125\) | \(8400000000000000\) | \([2]\) | \(196608\) | \(1.7638\) | |
| 33600.be3 | 33600b2 | \([0, -1, 0, -23633, -1330863]\) | \(5702413264/275625\) | \(70560000000000\) | \([2, 2]\) | \(98304\) | \(1.4172\) | |
| 33600.be4 | 33600b1 | \([0, -1, 0, 867, -81363]\) | \(4499456/180075\) | \(-2881200000000\) | \([2]\) | \(49152\) | \(1.0706\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33600.be have rank \(1\).
Complex multiplication
The elliptic curves in class 33600.be do not have complex multiplication.Modular form 33600.2.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.
