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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 85176.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 85176.br1 | 85176b1 | \([0, 0, 0, -1014, 10985]\) | \(55296/7\) | \(14596270416\) | \([2]\) | \(61440\) | \(0.67955\) | \(\Gamma_0(N)\)-optimal |
| 85176.br2 | 85176b2 | \([0, 0, 0, 1521, 57122]\) | \(11664/49\) | \(-1634782286592\) | \([2]\) | \(122880\) | \(1.0261\) |
Rank
sage: E.rank()
The elliptic curves in class 85176.br have rank \(1\).
Complex multiplication
The elliptic curves in class 85176.br do not have complex multiplication.Modular form 85176.2.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.
