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SageMath
E = EllipticCurve("bx1")
E.isogeny_class()
Elliptic curves in class 291312bx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
291312.bx1 | 291312bx1 | \([0, 0, 0, -15606, 663255]\) | \(55296/7\) | \(53211174310224\) | \([2]\) | \(983040\) | \(1.3630\) | \(\Gamma_0(N)\)-optimal |
291312.bx2 | 291312bx2 | \([0, 0, 0, 23409, 3448926]\) | \(11664/49\) | \(-5959651522745088\) | \([2]\) | \(1966080\) | \(1.7096\) |
Rank
sage: E.rank()
The elliptic curves in class 291312bx have rank \(0\).
Complex multiplication
The elliptic curves in class 291312bx do not have complex multiplication.Modular form 291312.2.a.bx
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.