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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 17640u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
17640.f2 | 17640u1 | \([0, 0, 0, 357, -2842]\) | \(19652/25\) | \(-6401203200\) | \([2]\) | \(9216\) | \(0.56763\) | \(\Gamma_0(N)\)-optimal |
17640.f1 | 17640u2 | \([0, 0, 0, -2163, -27538]\) | \(2185454/625\) | \(320060160000\) | \([2]\) | \(18432\) | \(0.91420\) |
Rank
sage: E.rank()
The elliptic curves in class 17640u have rank \(1\).
Complex multiplication
The elliptic curves in class 17640u do not have complex multiplication.Modular form 17640.2.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 Cremona 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 Cremona labels.