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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 265200cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
265200.cu2 | 265200cu1 | \([0, -1, 0, -1383, -14238]\) | \(1171019776/304317\) | \(76079250000\) | \([2]\) | \(163840\) | \(0.79697\) | \(\Gamma_0(N)\)-optimal |
265200.cu1 | 265200cu2 | \([0, -1, 0, -20508, -1123488]\) | \(238481570896/25857\) | \(103428000000\) | \([2]\) | \(327680\) | \(1.1435\) |
Rank
sage: E.rank()
The elliptic curves in class 265200cu have rank \(0\).
Complex multiplication
The elliptic curves in class 265200cu do not have complex multiplication.Modular form 265200.2.a.cu
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.