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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 84150.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 84150.br1 | 84150s2 | \([1, -1, 0, -8667, 312491]\) | \(170676802323/158950\) | \(67057031250\) | \([2]\) | \(147456\) | \(1.0002\) | |
| 84150.br2 | 84150s1 | \([1, -1, 0, -417, 7241]\) | \(-19034163/41140\) | \(-17355937500\) | \([2]\) | \(73728\) | \(0.65362\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 84150.br have rank \(1\).
Complex multiplication
The elliptic curves in class 84150.br do not have complex multiplication.Modular form 84150.2.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 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.
