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SageMath
E = EllipticCurve("hf1")
E.isogeny_class()
Elliptic curves in class 244800.hf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 244800.hf1 | 244800hf2 | \([0, 0, 0, -169500, 27830000]\) | \(-115431760/4913\) | \(-22922092800000000\) | \([]\) | \(1036800\) | \(1.9055\) | |
| 244800.hf2 | 244800hf1 | \([0, 0, 0, 10500, 110000]\) | \(27440/17\) | \(-79315200000000\) | \([]\) | \(345600\) | \(1.3562\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 244800.hf have rank \(0\).
Complex multiplication
The elliptic curves in class 244800.hf do not have complex multiplication.Modular form 244800.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
