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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 189618.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.u1 | 189618be1 | \([1, 0, 1, -152780, 22790666]\) | \(81706955619457/744505344\) | \(3593585094967296\) | \([2]\) | \(2419200\) | \(1.8070\) | \(\Gamma_0(N)\)-optimal |
189618.u2 | 189618be2 | \([1, 0, 1, -44620, 54459914]\) | \(-2035346265217/264305213568\) | \(-1275750783596944512\) | \([2]\) | \(4838400\) | \(2.1536\) |
Rank
sage: E.rank()
The elliptic curves in class 189618.u have rank \(1\).
Complex multiplication
The elliptic curves in class 189618.u do not have complex multiplication.Modular form 189618.2.a.u
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.