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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 176890cq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
176890.m2 | 176890cq1 | \([1, 0, 1, 562, -1032]\) | \(463391/280\) | \(-11891960920\) | \([]\) | \(124416\) | \(0.62251\) | \(\Gamma_0(N)\)-optimal |
176890.m1 | 176890cq2 | \([1, 0, 1, -8748, -328744]\) | \(-1742943169/85750\) | \(-3641913031750\) | \([]\) | \(373248\) | \(1.1718\) |
Rank
sage: E.rank()
The elliptic curves in class 176890cq have rank \(2\).
Complex multiplication
The elliptic curves in class 176890cq do not have complex multiplication.Modular form 176890.2.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 Cremona 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 Cremona labels.