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SageMath
E = EllipticCurve("cu1")
E.isogeny_class()
Elliptic curves in class 479370cu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
479370.cu2 | 479370cu1 | \([1, 0, 0, -82856, 10065216]\) | \(-105756712489/12476160\) | \(-7421110924527360\) | \([2]\) | \(4494336\) | \(1.7811\) | \(\Gamma_0(N)\)-optimal* |
479370.cu1 | 479370cu2 | \([1, 0, 0, -1361176, 611131280]\) | \(468898230633769/5540400\) | \(3295559127668400\) | \([2]\) | \(8988672\) | \(2.1276\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 479370cu have rank \(0\).
Complex multiplication
The elliptic curves in class 479370cu do not have complex multiplication.Modular form 479370.2.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.