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SageMath
E = EllipticCurve("by1")
E.isogeny_class()
Elliptic curves in class 18150.by
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18150.by1 | 18150ch4 | \([1, 1, 1, -2504763, -1521877719]\) | \(502270291349/1889568\) | \(6538056593062500000\) | \([2]\) | \(560000\) | \(2.4697\) | |
| 18150.by2 | 18150ch2 | \([1, 1, 1, -160388, 24653531]\) | \(131872229/18\) | \(62281441406250\) | \([2]\) | \(112000\) | \(1.6650\) | |
| 18150.by3 | 18150ch3 | \([1, 1, 1, -84763, -45677719]\) | \(-19465109/248832\) | \(-860978646000000000\) | \([2]\) | \(280000\) | \(2.1231\) | |
| 18150.by4 | 18150ch1 | \([1, 1, 1, -9138, 453531]\) | \(-24389/12\) | \(-41520960937500\) | \([2]\) | \(56000\) | \(1.3184\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 18150.by have rank \(0\).
Complex multiplication
The elliptic curves in class 18150.by do not have complex multiplication.Modular form 18150.2.a.by
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.
\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
