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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 17787.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17787.o1 | 17787u3 | \([1, 0, 0, -868722, 311273073]\) | \(347873904937/395307\) | \(82390825805842323\) | \([2]\) | \(207360\) | \(2.1593\) | |
17787.o2 | 17787u2 | \([1, 0, 0, -68307, 2152800]\) | \(169112377/88209\) | \(18384729725270601\) | \([2, 2]\) | \(103680\) | \(1.8127\) | |
17787.o3 | 17787u1 | \([1, 0, 0, -38662, -2904637]\) | \(30664297/297\) | \(61901446886433\) | \([2]\) | \(51840\) | \(1.4661\) | \(\Gamma_0(N)\)-optimal |
17787.o4 | 17787u4 | \([1, 0, 0, 257788, 16827075]\) | \(9090072503/5845851\) | \(-1218406179065660739\) | \([2]\) | \(207360\) | \(2.1593\) |
Rank
sage: E.rank()
The elliptic curves in class 17787.o have rank \(0\).
Complex multiplication
The elliptic curves in class 17787.o do not have complex multiplication.Modular form 17787.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.