Properties

Label 88935br
Number of curves $4$
Conductor $88935$
CM no
Rank $0$
Graph

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Show commands: 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)
 
\(q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + 3 q^{8} + q^{9} + q^{10} - q^{12} - 2 q^{13} - q^{15} - q^{16} - 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.