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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 189618.br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
189618.br1 | 189618j3 | \([1, 0, 0, -556892268, -5057497008240]\) | \(3957101249824708884951625/772310238681366528\) | \(3727794010859368089649152\) | \([2]\) | \(76640256\) | \(3.7145\) | |
189618.br2 | 189618j4 | \([1, 0, 0, -498053228, -6167895603312]\) | \(-2830680648734534916567625/1766676274677722124288\) | \(-8527408942700901249012436992\) | \([2]\) | \(153280512\) | \(4.0611\) | |
189618.br3 | 189618j1 | \([1, 0, 0, -16955013, 17399039553]\) | \(111675519439697265625/37528570137307392\) | \(181143240095886555472128\) | \([2]\) | \(25546752\) | \(3.1652\) | \(\Gamma_0(N)\)-optimal |
189618.br4 | 189618j2 | \([1, 0, 0, 49468747, 120262874289]\) | \(2773679829880629422375/2899504554614368272\) | \(-13995354679753624304604048\) | \([2]\) | \(51093504\) | \(3.5118\) |
Rank
sage: E.rank()
The elliptic curves in class 189618.br have rank \(0\).
Complex multiplication
The elliptic curves in class 189618.br do not have complex multiplication.Modular form 189618.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.