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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 474075.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
474075.z1 | 474075z2 | \([1, -1, 1, -911630, -333638378]\) | \(2315685267/9245\) | \(334507973334609375\) | \([2]\) | \(5308416\) | \(2.2194\) | |
474075.z2 | 474075z1 | \([1, -1, 1, -84755, 419122]\) | \(1860867/1075\) | \(38896275969140625\) | \([2]\) | \(2654208\) | \(1.8728\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 474075.z have rank \(1\).
Complex multiplication
The elliptic curves in class 474075.z do not have complex multiplication.Modular form 474075.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.