Properties

Label 14784.bq
Number of curves $4$
Conductor $14784$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bq1")
 
E.isogeny_class()
 

Elliptic curves in class 14784.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14784.bq1 14784cq3 \([0, 1, 0, -2575809, -1592036289]\) \(7209828390823479793/49509306\) \(12978567512064\) \([2]\) \(147456\) \(2.1160\)  
14784.bq2 14784cq4 \([0, 1, 0, -224449, -3556033]\) \(4770223741048753/2740574865798\) \(718425257619750912\) \([2]\) \(147456\) \(2.1160\)  
14784.bq3 14784cq2 \([0, 1, 0, -161089, -24883009]\) \(1763535241378513/4612311396\) \(1209089758593024\) \([2, 2]\) \(73728\) \(1.7694\)  
14784.bq4 14784cq1 \([0, 1, 0, -6209, -690753]\) \(-100999381393/723148272\) \(-189568980615168\) \([2]\) \(36864\) \(1.4228\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 14784.bq have rank \(1\).

Complex multiplication

The elliptic curves in class 14784.bq do not have complex multiplication.

Modular form 14784.2.a.bq

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.