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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5390.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5390.z1 | 5390bi2 | \([1, 1, 1, -21855, 1234477]\) | \(23560326604350529/1375000\) | \(67375000\) | \([]\) | \(7776\) | \(0.96704\) | |
5390.z2 | 5390bi1 | \([1, 1, 1, -295, 1245]\) | \(57954303169/17036800\) | \(834803200\) | \([]\) | \(2592\) | \(0.41773\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 5390.z have rank \(1\).
Complex multiplication
The elliptic curves in class 5390.z do not have complex multiplication.Modular form 5390.2.a.z
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.