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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 350064.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 350064.br1 | 350064br3 | \([0, 0, 0, -474511755, -3977821865158]\) | \(3957101249824708884951625/772310238681366528\) | \(2306106015738741550743552\) | \([2]\) | \(87588864\) | \(3.6745\) | |
| 350064.br2 | 350064br4 | \([0, 0, 0, -424376715, -4851184288966]\) | \(-2830680648734534916567625/1766676274677722124288\) | \(-5275267089367283419569979392\) | \([2]\) | \(175177728\) | \(4.0211\) | |
| 350064.br3 | 350064br1 | \([0, 0, 0, -14446875, 13685927114]\) | \(111675519439697265625/37528570137307392\) | \(112059709972877675593728\) | \([2]\) | \(29196288\) | \(3.1252\) | \(\Gamma_0(N)\)-optimal |
| 350064.br4 | 350064br2 | \([0, 0, 0, 42150885, 94586765258]\) | \(2773679829880629422375/2899504554614368272\) | \(-8657874208005629830299648\) | \([2]\) | \(58392576\) | \(3.4718\) |
Rank
sage: E.rank()
The elliptic curves in class 350064.br have rank \(1\).
Complex multiplication
The elliptic curves in class 350064.br do not have complex multiplication.Modular form 350064.2.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.
