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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 68208cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 68208.cn2 | 68208cq1 | \([0, 1, 0, -800, 3009012]\) | \(-117649/8118144\) | \(-3912054880075776\) | \([]\) | \(254016\) | \(1.6708\) | \(\Gamma_0(N)\)-optimal |
| 68208.cn1 | 68208cq2 | \([0, 1, 0, -5104640, -4453795788]\) | \(-30526075007211889/103499257854\) | \(-49875288831038447616\) | \([]\) | \(1778112\) | \(2.6437\) |
Rank
sage: E.rank()
The elliptic curves in class 68208cq have rank \(1\).
Complex multiplication
The elliptic curves in class 68208cq do not have complex multiplication.Modular form 68208.2.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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
