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SageMath
E = EllipticCurve("hz1")
E.isogeny_class()
Elliptic curves in class 103488.hz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 103488.hz1 | 103488df4 | \([0, 1, 0, -7454337, 7831115487]\) | \(2970658109581346/2139291\) | \(32988914890702848\) | \([2]\) | \(3145728\) | \(2.4814\) | |
| 103488.hz2 | 103488df3 | \([0, 1, 0, -1072577, -254298465]\) | \(8849350367426/3314597517\) | \(51112716963352805376\) | \([2]\) | \(3145728\) | \(2.4814\) | |
| 103488.hz3 | 103488df2 | \([0, 1, 0, -468897, 120586815]\) | \(1478729816932/38900169\) | \(299929828240982016\) | \([2, 2]\) | \(1572864\) | \(2.1349\) | |
| 103488.hz4 | 103488df1 | \([0, 1, 0, 5423, 6085967]\) | \(9148592/8301447\) | \(-16001547273879552\) | \([2]\) | \(786432\) | \(1.7883\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 103488.hz have rank \(1\).
Complex multiplication
The elliptic curves in class 103488.hz do not have complex multiplication.Modular form 103488.2.a.hz
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.
