Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 1680.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1680.q1 1680t5 \([0, 1, 0, -268800, 53550900]\) \(524388516989299201/3150\) \(12902400\) \([4]\) \(6144\) \(1.4299\)  
1680.q2 1680t4 \([0, 1, 0, -16800, 832500]\) \(128031684631201/9922500\) \(40642560000\) \([2, 4]\) \(3072\) \(1.0833\)  
1680.q3 1680t6 \([0, 1, 0, -15680, 949428]\) \(-104094944089921/35880468750\) \(-146966400000000\) \([8]\) \(6144\) \(1.4299\)  
1680.q4 1680t3 \([0, 1, 0, -5920, -167692]\) \(5602762882081/345888060\) \(1416757493760\) \([2]\) \(3072\) \(1.0833\)  
1680.q5 1680t2 \([0, 1, 0, -1120, 10868]\) \(37966934881/8643600\) \(35404185600\) \([2, 2]\) \(1536\) \(0.73676\)  
1680.q6 1680t1 \([0, 1, 0, 160, 1140]\) \(109902239/188160\) \(-770703360\) \([2]\) \(768\) \(0.39018\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1680.q do not have complex multiplication.

Modular form 1680.2.a.q

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

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.