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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 326700.cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 326700.cp1 | 326700cp1 | \([0, 0, 0, -217800, 39264500]\) | \(-5971968/25\) | \(-4783214700000000\) | \([]\) | \(1866240\) | \(1.8636\) | \(\Gamma_0(N)\)-optimal |
| 326700.cp2 | 326700cp2 | \([0, 0, 0, 508200, 206970500]\) | \(8429568/15625\) | \(-26905582687500000000\) | \([]\) | \(5598720\) | \(2.4129\) |
Rank
sage: E.rank()
The elliptic curves in class 326700.cp have rank \(1\).
Complex multiplication
The elliptic curves in class 326700.cp do not have complex multiplication.Modular form 326700.2.a.cp
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
