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SageMath
E = EllipticCurve("db1")
E.isogeny_class()
Elliptic curves in class 466752db
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 466752.db1 | 466752db1 | \([0, 1, 0, -5397633, -4828228641]\) | \(66342819962001390625/4812668669952\) | \(1261612215815897088\) | \([2]\) | \(11354112\) | \(2.5244\) | \(\Gamma_0(N)\)-optimal |
| 466752.db2 | 466752db2 | \([0, 1, 0, -5049473, -5477686305]\) | \(-54315282059491182625/17983956399469632\) | \(-4714386266382567211008\) | \([2]\) | \(22708224\) | \(2.8710\) |
Rank
sage: E.rank()
The elliptic curves in class 466752db have rank \(1\).
Complex multiplication
The elliptic curves in class 466752db do not have complex multiplication.Modular form 466752.2.a.db
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 Cremona 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 Cremona labels.
