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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 257600.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257600.u1 | 257600u1 | \([0, 1, 0, -56208, 5105338]\) | \(157114339136/181447\) | \(22680875000000\) | \([2]\) | \(860160\) | \(1.4754\) | \(\Gamma_0(N)\)-optimal |
257600.u2 | 257600u2 | \([0, 1, 0, -41833, 7793463]\) | \(-1012048064/2705927\) | \(-21647416000000000\) | \([2]\) | \(1720320\) | \(1.8219\) |
Rank
sage: E.rank()
The elliptic curves in class 257600.u have rank \(0\).
Complex multiplication
The elliptic curves in class 257600.u do not have complex multiplication.Modular form 257600.2.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.