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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 51984cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51984.z2 | 51984cq1 | \([0, 0, 0, 1022352, 454449904]\) | \(841232384/1121931\) | \(-157606901180488986624\) | \([]\) | \(1382400\) | \(2.5614\) | \(\Gamma_0(N)\)-optimal |
| 51984.z1 | 51984cq2 | \([0, 0, 0, -228227088, 1327088209264]\) | \(-9358714467168256/22284891\) | \(-3130542443033456062464\) | \([]\) | \(6912000\) | \(3.3661\) |
Rank
sage: E.rank()
The elliptic curves in class 51984cq have rank \(0\).
Complex multiplication
The elliptic curves in class 51984cq do not have complex multiplication.Modular form 51984.2.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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
