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SageMath
E = EllipticCurve("hl1")
E.isogeny_class()
Elliptic curves in class 446160.hl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
446160.hl1 | 446160hl2 | \([0, 1, 0, -79297560, 271766250900]\) | \(2789222297765780449/677605500\) | \(13396673846679552000\) | \([2]\) | \(37158912\) | \(3.0474\) | \(\Gamma_0(N)\)-optimal* |
446160.hl2 | 446160hl1 | \([0, 1, 0, -4937560, 4278458900]\) | \(-673350049820449/10617750000\) | \(-209919390759936000000\) | \([2]\) | \(18579456\) | \(2.7008\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 446160.hl have rank \(2\).
Complex multiplication
The elliptic curves in class 446160.hl do not have complex multiplication.Modular form 446160.2.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.