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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 132600br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 132600.cg1 | 132600br1 | \([0, 1, 0, -8908, -325312]\) | \(19545784144/89505\) | \(358020000000\) | \([2]\) | \(172032\) | \(1.0679\) | \(\Gamma_0(N)\)-optimal |
| 132600.cg2 | 132600br2 | \([0, 1, 0, -4408, -649312]\) | \(-592143556/10989225\) | \(-175827600000000\) | \([2]\) | \(344064\) | \(1.4144\) |
Rank
sage: E.rank()
The elliptic curves in class 132600br have rank \(1\).
Complex multiplication
The elliptic curves in class 132600br do not have complex multiplication.Modular form 132600.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
