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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 119952fp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
119952.y3 | 119952fp1 | \([0, 0, 0, 761901, -6907965806]\) | \(139233463487/58763045376\) | \(-20643342172350490607616\) | \([]\) | \(9953280\) | \(2.9609\) | \(\Gamma_0(N)\)-optimal |
119952.y2 | 119952fp2 | \([0, 0, 0, -6858579, 186739099666]\) | \(-101566487155393/42823570577256\) | \(-15043836050558885658525696\) | \([]\) | \(29859840\) | \(3.5102\) | |
119952.y1 | 119952fp3 | \([0, 0, 0, -2693289459, 53800653361714]\) | \(-6150311179917589675873/244053849830826\) | \(-85735637053876028399394816\) | \([]\) | \(89579520\) | \(4.0595\) |
Rank
sage: E.rank()
The elliptic curves in class 119952fp have rank \(0\).
Complex multiplication
The elliptic curves in class 119952fp do not have complex multiplication.Modular form 119952.2.a.fp
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.
\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.