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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 24882.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
24882.u1 | 24882u1 | \([1, 0, 1, -397, 3968]\) | \(-6894801108937/2926421784\) | \(-2926421784\) | \([3]\) | \(15552\) | \(0.52416\) | \(\Gamma_0(N)\)-optimal |
24882.u2 | 24882u2 | \([1, 0, 1, 3068, -44542]\) | \(3195164697368903/2715996501504\) | \(-2715996501504\) | \([]\) | \(46656\) | \(1.0735\) |
Rank
sage: E.rank()
The elliptic curves in class 24882.u have rank \(0\).
Complex multiplication
The elliptic curves in class 24882.u do not have complex multiplication.Modular form 24882.2.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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.