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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 9702.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9702.cf1 | 9702bp1 | \([1, -1, 1, -5081, -204991]\) | \(-3451273/2376\) | \(-9985234871304\) | \([]\) | \(24192\) | \(1.1947\) | \(\Gamma_0(N)\)-optimal |
| 9702.cf2 | 9702bp2 | \([1, -1, 1, 41224, 3073403]\) | \(1843623047/2044416\) | \(-8591739871486464\) | \([3]\) | \(72576\) | \(1.7440\) |
Rank
sage: E.rank()
The elliptic curves in class 9702.cf have rank \(0\).
Complex multiplication
The elliptic curves in class 9702.cf do not have complex multiplication.Modular form 9702.2.a.cf
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.
