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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 388080br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
388080.br3 | 388080br1 | \([0, 0, 0, -31458, -1831277]\) | \(2508888064/396165\) | \(543640565215440\) | \([2]\) | \(1179648\) | \(1.5502\) | \(\Gamma_0(N)\)-optimal |
388080.br2 | 388080br2 | \([0, 0, 0, -139503, 18286702]\) | \(13674725584/1334025\) | \(29290022289158400\) | \([2, 2]\) | \(2359296\) | \(1.8968\) | |
388080.br1 | 388080br3 | \([0, 0, 0, -2176923, 1236256378]\) | \(12990838708516/144375\) | \(12679663328640000\) | \([2]\) | \(4718592\) | \(2.2434\) | |
388080.br4 | 388080br4 | \([0, 0, 0, 169197, 87867682]\) | \(6099383804/41507235\) | \(-3645352488330685440\) | \([2]\) | \(4718592\) | \(2.2434\) |
Rank
sage: E.rank()
The elliptic curves in class 388080br have rank \(1\).
Complex multiplication
The elliptic curves in class 388080br do not have complex multiplication.Modular form 388080.2.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.