Properties

Label 6762.bl
Number of curves $6$
Conductor $6762$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("6762.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6762.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6762.bl1 6762bh5 [1, 0, 0, -3877567, 2938562717] [4] 196608  
6762.bl2 6762bh3 [1, 0, 0, -867987, -311320143] [2] 98304  
6762.bl3 6762bh4 [1, 0, 0, -248627, 43394385] [2, 2] 98304  
6762.bl4 6762bh2 [1, 0, 0, -56547, -4433535] [2, 2] 49152  
6762.bl5 6762bh1 [1, 0, 0, 6173, -381823] [2] 24576 \(\Gamma_0(N)\)-optimal
6762.bl6 6762bh6 [1, 0, 0, 307033, 209981253] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 6762.bl have rank \(0\).

Modular form 6762.2.a.bl

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + q^{8} + q^{9} + 2q^{10} - 4q^{11} + q^{12} + 2q^{13} + 2q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.