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SageMath
E = EllipticCurve("fy1")
E.isogeny_class()
Elliptic curves in class 77616.fy
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77616.fy1 | 77616gl2 | \([0, 0, 0, -1654779, 819327530]\) | \(1426487591593/2156\) | \(757398556164096\) | \([2]\) | \(884736\) | \(2.1231\) | |
77616.fy2 | 77616gl1 | \([0, 0, 0, -102459, 13052522]\) | \(-338608873/13552\) | \(-4760790924460032\) | \([2]\) | \(442368\) | \(1.7765\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 77616.fy have rank \(1\).
Complex multiplication
The elliptic curves in class 77616.fy do not have complex multiplication.Modular form 77616.2.a.fy
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.