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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 54760.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54760.b1 | 54760e1 | \([0, 1, 0, -82596, 9093760]\) | \(94875856/185\) | \(121512802730240\) | \([2]\) | \(262656\) | \(1.5911\) | \(\Gamma_0(N)\)-optimal |
54760.b2 | 54760e2 | \([0, 1, 0, -55216, 15248784]\) | \(-7086244/34225\) | \(-89919474020377600\) | \([2]\) | \(525312\) | \(1.9377\) |
Rank
sage: E.rank()
The elliptic curves in class 54760.b have rank \(0\).
Complex multiplication
The elliptic curves in class 54760.b do not have complex multiplication.Modular form 54760.2.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 LMFDB 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 LMFDB labels.