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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 29400ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 29400.m1 | 29400ct1 | \([0, -1, 0, -3450008, 2467266012]\) | \(7033666972/1215\) | \(784474120080000000\) | \([2]\) | \(645120\) | \(2.4396\) | \(\Gamma_0(N)\)-optimal |
| 29400.m2 | 29400ct2 | \([0, -1, 0, -3107008, 2976964012]\) | \(-2568731006/1476225\) | \(-1906272111794400000000\) | \([2]\) | \(1290240\) | \(2.7862\) |
Rank
sage: E.rank()
The elliptic curves in class 29400ct have rank \(1\).
Complex multiplication
The elliptic curves in class 29400ct do not have complex multiplication.Modular form 29400.2.a.ct
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
