Properties

Label 88935.bv
Number of curves $6$
Conductor $88935$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("88935.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 88935.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
88935.bv1 88935bq6 [1, 0, 1, -78559374, -268000082759] [2] 11796480  
88935.bv2 88935bq4 [1, 0, 1, -5187999, -3687041459] [2, 2] 5898240  
88935.bv3 88935bq2 [1, 0, 1, -1600954, 727893527] [2, 2] 2949120  
88935.bv4 88935bq1 [1, 0, 1, -1571309, 757989131] [2] 1474560 \(\Gamma_0(N)\)-optimal
88935.bv5 88935bq3 [1, 0, 1, 1511771, 3216828437] [2] 5898240  
88935.bv6 88935bq5 [1, 0, 1, 10790656, -21915491083] [2] 11796480  

Rank

sage: E.rank()
 

The elliptic curves in class 88935.bv have rank \(0\).

Modular form 88935.2.a.bv

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.