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SageMath
E = EllipticCurve("cy1")
E.isogeny_class()
Elliptic curves in class 190608.cy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190608.cy1 | 190608z2 | \([0, 1, 0, -4452, -55848]\) | \(810448/363\) | \(4371879629568\) | \([2]\) | \(314496\) | \(1.1209\) | |
190608.cy2 | 190608z1 | \([0, 1, 0, 963, -6030]\) | \(131072/99\) | \(-74520675504\) | \([2]\) | \(157248\) | \(0.77435\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 190608.cy have rank \(0\).
Complex multiplication
The elliptic curves in class 190608.cy do not have complex multiplication.Modular form 190608.2.a.cy
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.