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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 350064.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
350064.u1 | 350064u1 | \([0, 0, 0, -126, -505]\) | \(512096256/41327\) | \(17853264\) | \([2]\) | \(98304\) | \(0.13453\) | \(\Gamma_0(N)\)-optimal |
350064.u2 | 350064u2 | \([0, 0, 0, 129, -2290]\) | \(34347024/347633\) | \(-2402839296\) | \([2]\) | \(196608\) | \(0.48110\) |
Rank
sage: E.rank()
The elliptic curves in class 350064.u have rank \(1\).
Complex multiplication
The elliptic curves in class 350064.u do not have complex multiplication.Modular form 350064.2.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.