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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 121275.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121275.br1 | 121275eo4 | \([1, -1, 1, -9713255, 11654236122]\) | \(75627935783569/396165\) | \(530898989468203125\) | \([2]\) | \(3538944\) | \(2.5971\) | |
| 121275.br2 | 121275eo2 | \([1, -1, 1, -617630, 175557372]\) | \(19443408769/1334025\) | \(1787721086984765625\) | \([2, 2]\) | \(1769472\) | \(2.2506\) | |
| 121275.br3 | 121275eo1 | \([1, -1, 1, -121505, -12970128]\) | \(148035889/31185\) | \(41790882552890625\) | \([2]\) | \(884736\) | \(1.9040\) | \(\Gamma_0(N)\)-optimal |
| 121275.br4 | 121275eo3 | \([1, -1, 1, 539995, 756685122]\) | \(12994449551/192163125\) | \(-257516966101376953125\) | \([2]\) | \(3538944\) | \(2.5971\) |
Rank
sage: E.rank()
The elliptic curves in class 121275.br have rank \(2\).
Complex multiplication
The elliptic curves in class 121275.br do not have complex multiplication.Modular form 121275.2.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.
