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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 439569.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
439569.q1 | 439569q2 | \([1, -1, 1, -32976833, 405266116610]\) | \(-276301129/4782969\) | \(-68653936045298780883672849\) | \([]\) | \(76876800\) | \(3.6388\) | \(\Gamma_0(N)\)-optimal* |
439569.q2 | 439569q1 | \([1, -1, 1, -4404848, -3598988740]\) | \(-658489/9\) | \(-129184492813499110689\) | \([]\) | \(10982400\) | \(2.6658\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 439569.q have rank \(0\).
Complex multiplication
The elliptic curves in class 439569.q do not have complex multiplication.Modular form 439569.2.a.q
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.