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SageMath
E = EllipticCurve("hf1")
E.isogeny_class()
Elliptic curves in class 58800.hf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
58800.hf1 | 58800cv2 | \([0, 1, 0, -157208, 21267588]\) | \(665500/81\) | \(52298274672000000\) | \([2]\) | \(516096\) | \(1.9384\) | |
58800.hf2 | 58800cv1 | \([0, 1, 0, 14292, 1716588]\) | \(2000/9\) | \(-1452729852000000\) | \([2]\) | \(258048\) | \(1.5918\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 58800.hf have rank \(1\).
Complex multiplication
The elliptic curves in class 58800.hf do not have complex multiplication.Modular form 58800.2.a.hf
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.