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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 5054b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5054.b2 | 5054b1 | \([1, -1, 1, 20148, 32163887]\) | \(53261199/26353376\) | \(-447574222639176416\) | \([]\) | \(47880\) | \(2.0660\) | \(\Gamma_0(N)\)-optimal |
| 5054.b1 | 5054b2 | \([1, -1, 1, -27347262, -55124114227]\) | \(-133179212896925841/240518168576\) | \(-4084855478516361199616\) | \([]\) | \(335160\) | \(3.0389\) |
Rank
sage: E.rank()
The elliptic curves in class 5054b have rank \(1\).
Complex multiplication
The elliptic curves in class 5054b do not have complex multiplication.Modular form 5054.2.a.b
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.
\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
