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SageMath
E = EllipticCurve("hl1")
E.isogeny_class()
Elliptic curves in class 430950.hl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
430950.hl1 | 430950hl2 | \([1, 0, 0, -21188463, 37535838417]\) | \(6349095794413/520200\) | \(86194696466165625000\) | \([2]\) | \(31629312\) | \(2.8700\) | \(\Gamma_0(N)\)-optimal* |
430950.hl2 | 430950hl1 | \([1, 0, 0, -1415463, 501009417]\) | \(1892819053/440640\) | \(73011978183105000000\) | \([2]\) | \(15814656\) | \(2.5234\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 430950.hl have rank \(0\).
Complex multiplication
The elliptic curves in class 430950.hl do not have complex multiplication.Modular form 430950.2.a.hl
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.