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SageMath
E = EllipticCurve("d1")
E.isogeny_class()
Elliptic curves in class 160446.d
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
160446.d1 | 160446bq1 | \([1, 1, 0, -10204900, 12542579152]\) | \(66342819962001390625/4812668669952\) | \(8525936121608835072\) | \([2]\) | \(7096320\) | \(2.6836\) | \(\Gamma_0(N)\)-optimal |
160446.d2 | 160446bq2 | \([1, 1, 0, -9546660, 14231491344]\) | \(-54315282059491182625/17983956399469632\) | \(-31859675783000820735552\) | \([2]\) | \(14192640\) | \(3.0302\) |
Rank
sage: E.rank()
The elliptic curves in class 160446.d have rank \(0\).
Complex multiplication
The elliptic curves in class 160446.d do not have complex multiplication.Modular form 160446.2.a.d
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.