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SageMath
E = EllipticCurve("ba1")
E.isogeny_class()
Elliptic curves in class 457776ba
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
457776.ba2 | 457776ba1 | \([0, 0, 0, -1901331, -996739614]\) | \(8586756/121\) | \(10711570429874045952\) | \([2]\) | \(11698176\) | \(2.4564\) | \(\Gamma_0(N)\)-optimal* |
457776.ba1 | 457776ba2 | \([0, 0, 0, -3670011, 1150084170]\) | \(30876498/14641\) | \(2592200044029519120384\) | \([2]\) | \(23396352\) | \(2.8030\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 457776ba have rank \(0\).
Complex multiplication
The elliptic curves in class 457776ba do not have complex multiplication.Modular form 457776.2.a.ba
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.