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SageMath
E = EllipticCurve("fl1")
E.isogeny_class()
Elliptic curves in class 466578.fl
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
466578.fl1 | 466578fl2 | \([1, -1, 1, -780706499, -7334539847197]\) | \(4144806984356137/568114785504\) | \(7213048904019432249404215776\) | \([2]\) | \(389283840\) | \(4.0723\) | \(\Gamma_0(N)\)-optimal* |
466578.fl2 | 466578fl1 | \([1, -1, 1, 77797021, -610396877149]\) | \(4101378352343/15049939968\) | \(-191081020529039417469729792\) | \([2]\) | \(194641920\) | \(3.7258\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 466578.fl have rank \(1\).
Complex multiplication
The elliptic curves in class 466578.fl do not have complex multiplication.Modular form 466578.2.a.fl
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.