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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 19890.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 19890.p1 | 19890n1 | \([1, -1, 0, -2754, -31212]\) | \(3169397364769/1231093760\) | \(897467351040\) | \([2]\) | \(24576\) | \(0.99241\) | \(\Gamma_0(N)\)-optimal |
| 19890.p2 | 19890n2 | \([1, -1, 0, 8766, -231660]\) | \(102181603702751/90336313600\) | \(-65855172614400\) | \([2]\) | \(49152\) | \(1.3390\) |
Rank
sage: E.rank()
The elliptic curves in class 19890.p have rank \(1\).
Complex multiplication
The elliptic curves in class 19890.p do not have complex multiplication.Modular form 19890.2.a.p
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.
