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SageMath
E = EllipticCurve("jj1")
E.isogeny_class()
Elliptic curves in class 474320.jj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474320.jj1 | 474320jj1 | \([0, 0, 0, -254947, -49547806]\) | \(-5154200289/20\) | \(-7111187578880\) | \([]\) | \(4032000\) | \(1.6793\) | \(\Gamma_0(N)\)-optimal* |
474320.jj2 | 474320jj2 | \([0, 0, 0, 1777853, 470117186]\) | \(1747829720511/1280000000\) | \(-455116005048320000000\) | \([]\) | \(28224000\) | \(2.6522\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 474320.jj have rank \(1\).
Complex multiplication
The elliptic curves in class 474320.jj do not have complex multiplication.Modular form 474320.2.a.jj
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.