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SageMath
E = EllipticCurve("cx1")
E.isogeny_class()
Elliptic curves in class 188760cx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
188760.w2 | 188760cx1 | \([0, -1, 0, -186182256, -11914406961444]\) | \(-393443624385770851876/33577011001321734375\) | \(-60911332542988833864816000000\) | \([2]\) | \(143769600\) | \(4.2029\) | \(\Gamma_0(N)\)-optimal |
188760.w1 | 188760cx2 | \([0, -1, 0, -9043987256, -328701401859444]\) | \(22548490527122525577915938/183925440576065170125\) | \(667310361461503157968517376000\) | \([2]\) | \(287539200\) | \(4.5495\) |
Rank
sage: E.rank()
The elliptic curves in class 188760cx have rank \(1\).
Complex multiplication
The elliptic curves in class 188760cx do not have complex multiplication.Modular form 188760.2.a.cx
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.