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SageMath
E = EllipticCurve("co1")
E.isogeny_class()
Elliptic curves in class 76050.co
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 76050.co1 | 76050bl2 | \([1, -1, 0, -1749942, 798626466]\) | \(10779215329/1232010\) | \(67736367202962656250\) | \([2]\) | \(3096576\) | \(2.5375\) | |
| 76050.co2 | 76050bl1 | \([1, -1, 0, 151308, 62842716]\) | \(6967871/35100\) | \(-1929811031423437500\) | \([2]\) | \(1548288\) | \(2.1909\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 76050.co have rank \(0\).
Complex multiplication
The elliptic curves in class 76050.co do not have complex multiplication.Modular form 76050.2.a.co
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.
