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SageMath
E = EllipticCurve("bk1")
E.isogeny_class()
Elliptic curves in class 476520bk
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 476520.bk1 | 476520bk1 | \([0, 1, 0, -3946211, 3015984354]\) | \(9028656748079104/3969405\) | \(2987906484332880\) | \([2]\) | \(9289728\) | \(2.3109\) | \(\Gamma_0(N)\)-optimal |
| 476520.bk2 | 476520bk2 | \([0, 1, 0, -3926356, 3047855600]\) | \(-555816294307024/11837848275\) | \(-142572032317876550400\) | \([2]\) | \(18579456\) | \(2.6574\) |
Rank
sage: E.rank()
The elliptic curves in class 476520bk have rank \(1\).
Complex multiplication
The elliptic curves in class 476520bk do not have complex multiplication.Modular form 476520.2.a.bk
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.
