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SageMath
E = EllipticCurve("o1")
E.isogeny_class()
Elliptic curves in class 466752.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466752.o1 | 466752o4 | \([0, -1, 0, -18689, -975807]\) | \(22032065143304/35830509\) | \(1174094118912\) | \([2]\) | \(802816\) | \(1.2128\) | |
466752.o2 | 466752o2 | \([0, -1, 0, -1529, -4551]\) | \(96576225472/53187849\) | \(217857429504\) | \([2, 2]\) | \(401408\) | \(0.86618\) | |
466752.o3 | 466752o1 | \([0, -1, 0, -924, 11058]\) | \(1364676090688/9706983\) | \(621246912\) | \([2]\) | \(200704\) | \(0.51961\) | \(\Gamma_0(N)\)-optimal* |
466752.o4 | 466752o3 | \([0, -1, 0, 5951, -41951]\) | \(711165446776/432613467\) | \(-14175878086656\) | \([2]\) | \(802816\) | \(1.2128\) |
Rank
sage: E.rank()
The elliptic curves in class 466752.o have rank \(1\).
Complex multiplication
The elliptic curves in class 466752.o do not have complex multiplication.Modular form 466752.2.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.