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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 169932.o
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169932.o1 | 169932bh1 | \([0, -1, 0, -4776977, 4016327610]\) | \(265327034368/297381\) | \(13511854766469104976\) | \([2]\) | \(4976640\) | \(2.5849\) | \(\Gamma_0(N)\)-optimal |
| 169932.o2 | 169932bh2 | \([0, -1, 0, -3573292, 6088110232]\) | \(-6940769488/18000297\) | \(-13085833933832196724992\) | \([2]\) | \(9953280\) | \(2.9315\) |
Rank
sage: E.rank()
The elliptic curves in class 169932.o have rank \(1\).
Complex multiplication
The elliptic curves in class 169932.o do not have complex multiplication.Modular form 169932.2.a.o
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.
