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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 466752.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 466752.k1 | 466752k1 | \([0, -1, 0, -2029, 35725]\) | \(902576293888/4091373\) | \(4189565952\) | \([2]\) | \(294912\) | \(0.69762\) | \(\Gamma_0(N)\)-optimal |
| 466752.k2 | 466752k2 | \([0, -1, 0, -1009, 70609]\) | \(-6940769488/126190779\) | \(-2067509723136\) | \([2]\) | \(589824\) | \(1.0442\) |
Rank
sage: E.rank()
The elliptic curves in class 466752.k have rank \(2\).
Complex multiplication
The elliptic curves in class 466752.k do not have complex multiplication.Modular form 466752.2.a.k
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
