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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 259920.cu
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 259920.cu1 | 259920cu2 | \([0, 0, 0, -1560603, 738563402]\) | \(2992209121/54150\) | \(7606897125512601600\) | \([2]\) | \(6635520\) | \(2.4182\) | |
| 259920.cu2 | 259920cu1 | \([0, 0, 0, -1083, 33348458]\) | \(-1/3420\) | \(-480435607927111680\) | \([2]\) | \(3317760\) | \(2.0717\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 259920.cu have rank \(2\).
Complex multiplication
The elliptic curves in class 259920.cu do not have complex multiplication.Modular form 259920.2.a.cu
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.
