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SageMath
E = EllipticCurve("gq1")
E.isogeny_class()
Elliptic curves in class 476850.gq
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
476850.gq1 | 476850gq2 | \([1, 1, 1, -5195559063, -143602435995219]\) | \(41125104693338423360329/179205840000000000\) | \(67587395753171250000000000000\) | \([2]\) | \(690094080\) | \(4.3849\) | \(\Gamma_0(N)\)-optimal* |
476850.gq2 | 476850gq1 | \([1, 1, 1, -164647063, -4457471899219]\) | \(-1308796492121439049/22000592486400000\) | \(-8297512799708774400000000000\) | \([2]\) | \(345047040\) | \(4.0384\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 476850.gq have rank \(1\).
Complex multiplication
The elliptic curves in class 476850.gq do not have complex multiplication.Modular form 476850.2.a.gq
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.