Properties

Label 1680.q
Number of curves $6$
Conductor $1680$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1680.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1680.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1680.q1 1680t5 [0, 1, 0, -268800, 53550900] [4] 6144  
1680.q2 1680t4 [0, 1, 0, -16800, 832500] [2, 4] 3072  
1680.q3 1680t6 [0, 1, 0, -15680, 949428] [8] 6144  
1680.q4 1680t3 [0, 1, 0, -5920, -167692] [2] 3072  
1680.q5 1680t2 [0, 1, 0, -1120, 10868] [2, 2] 1536  
1680.q6 1680t1 [0, 1, 0, 160, 1140] [2] 768 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1680.q have rank \(0\).

Modular form 1680.2.a.q

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} - 4q^{11} - 2q^{13} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.