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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 63175.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63175.n1 | 63175d3 | \([0, 1, 1, -1185283, 519182094]\) | \(-250523582464/13671875\) | \(-10050084442138671875\) | \([]\) | \(1026432\) | \(2.4044\) | |
63175.n2 | 63175d1 | \([0, 1, 1, -12033, -567656]\) | \(-262144/35\) | \(-25728216171875\) | \([]\) | \(114048\) | \(1.3058\) | \(\Gamma_0(N)\)-optimal |
63175.n3 | 63175d2 | \([0, 1, 1, 78217, 1462969]\) | \(71991296/42875\) | \(-31517064810546875\) | \([]\) | \(342144\) | \(1.8551\) |
Rank
sage: E.rank()
The elliptic curves in class 63175.n have rank \(0\).
Complex multiplication
The elliptic curves in class 63175.n do not have complex multiplication.Modular form 63175.2.a.n
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.