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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 7056.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7056.br1 | 7056v3 | \([0, 0, 0, -67179, -6693302]\) | \(381775972/567\) | \(49796495981568\) | \([2]\) | \(24576\) | \(1.5292\) | |
7056.br2 | 7056v2 | \([0, 0, 0, -5439, -37730]\) | \(810448/441\) | \(9682651996416\) | \([2, 2]\) | \(12288\) | \(1.1826\) | |
7056.br3 | 7056v1 | \([0, 0, 0, -3234, 70315]\) | \(2725888/21\) | \(28817416656\) | \([2]\) | \(6144\) | \(0.83607\) | \(\Gamma_0(N)\)-optimal |
7056.br4 | 7056v4 | \([0, 0, 0, 21021, -297038]\) | \(11696828/7203\) | \(-632599930432512\) | \([2]\) | \(24576\) | \(1.5292\) |
Rank
sage: E.rank()
The elliptic curves in class 7056.br have rank \(1\).
Complex multiplication
The elliptic curves in class 7056.br do not have complex multiplication.Modular form 7056.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.