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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 349830.k
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 349830.k1 | 349830k2 | \([1, -1, 0, -8875320, 10176482096]\) | \(813812572383147/262761200\) | \(24963911994587576400\) | \([2]\) | \(17547264\) | \(2.6963\) | |
| 349830.k2 | 349830k1 | \([1, -1, 0, -479400, 203808320]\) | \(-128252814507/114433280\) | \(-10871857531370684160\) | \([2]\) | \(8773632\) | \(2.3498\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 349830.k have rank \(1\).
Complex multiplication
The elliptic curves in class 349830.k do not have complex multiplication.Modular form 349830.2.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.
