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SageMath
E = EllipticCurve("bb1")
E.isogeny_class()
Elliptic curves in class 81225.bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81225.bb1 | 81225y2 | \([0, 0, 1, -65550, -4809969]\) | \(7575076864/1953125\) | \(8031280517578125\) | \([]\) | \(435456\) | \(1.7611\) | |
81225.bb2 | 81225y1 | \([0, 0, 1, -22800, 1324656]\) | \(318767104/125\) | \(514001953125\) | \([]\) | \(145152\) | \(1.2118\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 81225.bb have rank \(1\).
Complex multiplication
The elliptic curves in class 81225.bb do not have complex multiplication.Modular form 81225.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.