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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 63175.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
63175.x1 | 63175y2 | \([0, 1, 1, -53548, -4811211]\) | \(-2887553024/16807\) | \(-98837515245875\) | \([]\) | \(288000\) | \(1.5264\) | |
63175.x2 | 63175y1 | \([0, 1, 1, 602, 8139]\) | \(4096/7\) | \(-41165145875\) | \([]\) | \(57600\) | \(0.72169\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 63175.x have rank \(0\).
Complex multiplication
The elliptic curves in class 63175.x do not have complex multiplication.Modular form 63175.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.