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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 162240bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162240.ej2 | 162240bb1 | \([0, 1, 0, 49799, 7057415]\) | \(314432/675\) | \(-29319319866470400\) | \([2]\) | \(1677312\) | \(1.8440\) | \(\Gamma_0(N)\)-optimal |
162240.ej1 | 162240bb2 | \([0, 1, 0, -389601, 76218975]\) | \(18821096/3645\) | \(1266594618231521280\) | \([2]\) | \(3354624\) | \(2.1906\) |
Rank
sage: E.rank()
The elliptic curves in class 162240bb have rank \(0\).
Complex multiplication
The elliptic curves in class 162240bb do not have complex multiplication.Modular form 162240.2.a.bb
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.