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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 3200.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3200.x1 | 3200t2 | \([0, -1, 0, -233, 1337]\) | \(10976\) | \(128000000\) | \([2]\) | \(1024\) | \(0.29486\) | |
3200.x2 | 3200t1 | \([0, -1, 0, 17, 87]\) | \(128\) | \(-4000000\) | \([2]\) | \(512\) | \(-0.051711\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 3200.x have rank \(0\).
Complex multiplication
The elliptic curves in class 3200.x do not have complex multiplication.Modular form 3200.2.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.