Properties

Label 88935.bq
Number of curves $6$
Conductor $88935$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88935.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88935.bq1 88935m6 [1, 1, 0, -18078706923, -935626807637892] [2] 44236800  
88935.bq2 88935m4 [1, 1, 0, -1129919298, -14619518822817] [2, 2] 22118400  
88935.bq3 88935m5 [1, 1, 0, -1124316393, -14771672431578] [2] 44236800  
88935.bq4 88935m3 [1, 1, 0, -150863528, 376052042997] [2] 22118400  
88935.bq5 88935m2 [1, 1, 0, -70970253, -226071613368] [2, 2] 11059200  
88935.bq6 88935m1 [1, 1, 0, 207392, -10559939837] [2] 5529600 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 88935.bq have rank \(1\).

Complex multiplication

The elliptic curves in class 88935.bq do not have complex multiplication.

Modular form 88935.2.a.bq

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} - q^{4} - q^{5} - q^{6} - 3q^{8} + q^{9} - q^{10} + q^{12} - 2q^{13} + q^{15} - q^{16} + 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.