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SageMath
E = EllipticCurve("ha1")
E.isogeny_class()
Elliptic curves in class 73920.ha
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 73920.ha1 | 73920hq2 | \([0, 1, 0, -9525, 979923]\) | \(-5833703071744/22107421875\) | \(-362208000000000\) | \([]\) | \(248832\) | \(1.4792\) | |
| 73920.ha2 | 73920hq1 | \([0, 1, 0, 1035, -31725]\) | \(7476617216/31444875\) | \(-515192832000\) | \([]\) | \(82944\) | \(0.92990\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 73920.ha have rank \(1\).
Complex multiplication
The elliptic curves in class 73920.ha do not have complex multiplication.Modular form 73920.2.a.ha
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.
