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SageMath
E = EllipticCurve("hh1")
E.isogeny_class()
Elliptic curves in class 432450.hh
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
432450.hh1 | 432450hh2 | \([1, -1, 1, -142929230, -657666575103]\) | \(31942518433489/27900\) | \(282047283097298437500\) | \([2]\) | \(58982400\) | \(3.2244\) | \(\Gamma_0(N)\)-optimal* |
432450.hh2 | 432450hh1 | \([1, -1, 1, -8869730, -10427309103]\) | \(-7633736209/230640\) | \(-2331590873604333750000\) | \([2]\) | \(29491200\) | \(2.8779\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 432450.hh have rank \(0\).
Complex multiplication
The elliptic curves in class 432450.hh do not have complex multiplication.Modular form 432450.2.a.hh
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.