Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("1680.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1680.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1680.t1 1680j5 [0, 1, 0, -10480, 409460] [4] 2048  
1680.t2 1680j3 [0, 1, 0, -680, 5700] [2, 4] 1024  
1680.t3 1680j2 [0, 1, 0, -180, -900] [2, 2] 512  
1680.t4 1680j1 [0, 1, 0, -175, -952] [2] 256 \(\Gamma_0(N)\)-optimal
1680.t5 1680j4 [0, 1, 0, 240, -4092] [2] 1024  
1680.t6 1680j6 [0, 1, 0, 1120, 32340] [4] 2048  

Rank

sage: E.rank()
 

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

Modular form 1680.2.a.t

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.