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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 33150.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33150.x1 | 33150w2 | \([1, 0, 1, -422326, -63888952]\) | \(4265163186671717/1566431677824\) | \(3059436870750000000\) | \([2]\) | \(483840\) | \(2.2473\) | |
33150.x2 | 33150w1 | \([1, 0, 1, -182326, 29231048]\) | \(343191135492197/9417867264\) | \(18394272000000000\) | \([2]\) | \(241920\) | \(1.9007\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 33150.x have rank \(1\).
Complex multiplication
The elliptic curves in class 33150.x do not have complex multiplication.Modular form 33150.2.a.x
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.