Properties

Label 33600.fp
Number of curves $4$
Conductor $33600$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("fp1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600.fp

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.fp1 33600gx4 \([0, 1, 0, -112033, 14396063]\) \(303735479048/105\) \(53760000000\) \([2]\) \(147456\) \(1.4149\)  
33600.fp2 33600gx2 \([0, 1, 0, -7033, 221063]\) \(601211584/11025\) \(705600000000\) \([2, 2]\) \(73728\) \(1.0683\)  
33600.fp3 33600gx1 \([0, 1, 0, -908, -5562]\) \(82881856/36015\) \(36015000000\) \([2]\) \(36864\) \(0.72173\) \(\Gamma_0(N)\)-optimal
33600.fp4 33600gx3 \([0, 1, 0, -33, 648063]\) \(-8/354375\) \(-181440000000000\) \([2]\) \(147456\) \(1.4149\)  

Rank

sage: E.rank()
 

The elliptic curves in class 33600.fp have rank \(0\).

Complex multiplication

The elliptic curves in class 33600.fp do not have complex multiplication.

Modular form 33600.2.a.fp

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - 4q^{11} + 6q^{13} + 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.