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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 157170.cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
157170.cq1 | 157170v2 | \([1, 0, 0, -88306, -10109620]\) | \(-15777367606441/3574920\) | \(-17255456030280\) | \([]\) | \(829440\) | \(1.5321\) | |
157170.cq2 | 157170v1 | \([1, 0, 0, 419, -48205]\) | \(1685159/209250\) | \(-1010009783250\) | \([]\) | \(276480\) | \(0.98277\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 157170.cq have rank \(1\).
Complex multiplication
The elliptic curves in class 157170.cq do not have complex multiplication.Modular form 157170.2.a.cq
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.