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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 184041br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
184041.bs2 | 184041br1 | \([1, -1, 0, -3834, 358177]\) | \(-121\) | \(-51517927404801\) | \([]\) | \(336960\) | \(1.3138\) | \(\Gamma_0(N)\)-optimal |
184041.bs1 | 184041br2 | \([1, -1, 0, -5525064, -4997459219]\) | \(-24729001\) | \(-754273975133691441\) | \([]\) | \(3706560\) | \(2.5128\) |
Rank
sage: E.rank()
The elliptic curves in class 184041br have rank \(1\).
Complex multiplication
The elliptic curves in class 184041br do not have complex multiplication.Modular form 184041.2.a.br
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.