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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 117117br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117117.bm2 | 117117br1 | \([1, -1, 0, 5292, -563549]\) | \(4657463/41503\) | \(-146038422312783\) | \([2]\) | \(311040\) | \(1.3992\) | \(\Gamma_0(N)\)-optimal |
117117.bm1 | 117117br2 | \([1, -1, 0, -78363, -7774610]\) | \(15124197817/1294139\) | \(4553743532116779\) | \([2]\) | \(622080\) | \(1.7458\) |
Rank
sage: E.rank()
The elliptic curves in class 117117br have rank \(0\).
Complex multiplication
The elliptic curves in class 117117br do not have complex multiplication.Modular form 117117.2.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.