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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 17472cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 17472.bs3 | 17472cq1 | \([0, 1, 0, 863, -92449]\) | \(270840023/14329224\) | \(-3756320096256\) | \([]\) | \(41472\) | \(1.0926\) | \(\Gamma_0(N)\)-optimal |
| 17472.bs2 | 17472cq2 | \([0, 1, 0, -7777, 2525471]\) | \(-198461344537/10417365504\) | \(-2730849862680576\) | \([]\) | \(124416\) | \(1.6419\) | |
| 17472.bs1 | 17472cq3 | \([0, 1, 0, -1667617, 828339551]\) | \(-1956469094246217097/36641439744\) | \(-9605333580251136\) | \([]\) | \(373248\) | \(2.1912\) |
Rank
sage: E.rank()
The elliptic curves in class 17472cq have rank \(1\).
Complex multiplication
The elliptic curves in class 17472cq do not have complex multiplication.Modular form 17472.2.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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
