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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 88935br
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88935.s3 | 88935br1 | \([1, 0, 0, -96301906, -363755876989]\) | \(473897054735271721/779625\) | \(162491298076886625\) | \([2]\) | \(6635520\) | \(2.9942\) | \(\Gamma_0(N)\)-optimal |
88935.s2 | 88935br2 | \([1, 0, 0, -96331551, -363520726920]\) | \(474334834335054841/607815140625\) | \(126682278263192735015625\) | \([2, 2]\) | \(13271040\) | \(3.3408\) | |
88935.s4 | 88935br3 | \([1, 0, 0, -70392176, -563684508045]\) | \(-185077034913624841/551466161890875\) | \(-114937889999841956190787875\) | \([2]\) | \(26542080\) | \(3.6874\) | |
88935.s1 | 88935br4 | \([1, 0, 0, -122745246, -148307222799]\) | \(981281029968144361/522287841796875\) | \(108856475078851781982421875\) | \([2]\) | \(26542080\) | \(3.6874\) |
Rank
sage: E.rank()
The elliptic curves in class 88935br have rank \(0\).
Complex multiplication
The elliptic curves in class 88935br do not have complex multiplication.Modular form 88935.2.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.