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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 339864br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
339864.br4 | 339864br1 | \([0, 1, 0, -10006790404, -388875419153824]\) | \(-152435594466395827792/1646846627220711\) | \(-1197222550178026610001132746496\) | \([4]\) | \(477757440\) | \(4.5874\) | \(\Gamma_0(N)\)-optimal |
339864.br3 | 339864br2 | \([0, 1, 0, -160521510424, -24754198295991424]\) | \(157304700372188331121828/18069292138401\) | \(52543967741202302140155577344\) | \([2, 2]\) | \(955514880\) | \(4.9340\) | |
339864.br2 | 339864br3 | \([0, 1, 0, -160934445184, -24620438156097568]\) | \(79260902459030376659234/842751810121431609\) | \(4901301455052897358729191377160192\) | \([2]\) | \(1911029760\) | \(5.2806\) | |
339864.br1 | 339864br4 | \([0, 1, 0, -2568344095984, -1584266214317971360]\) | \(322159999717985454060440834/4250799\) | \(24721925332720884774912\) | \([2]\) | \(1911029760\) | \(5.2806\) |
Rank
sage: E.rank()
The elliptic curves in class 339864br have rank \(0\).
Complex multiplication
The elliptic curves in class 339864br do not have complex multiplication.Modular form 339864.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.