Properties

Label 33600gh
Number of curves $4$
Conductor $33600$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("gh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 33600gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
33600.dy3 33600gh1 [0, 1, 0, -5633, 100863] [2] 73728 \(\Gamma_0(N)\)-optimal
33600.dy2 33600gh2 [0, 1, 0, -37633, -2747137] [2, 2] 147456  
33600.dy4 33600gh3 [0, 1, 0, 10367, -9227137] [2] 294912  
33600.dy1 33600gh4 [0, 1, 0, -597633, -178027137] [2] 294912  

Rank

sage: E.rank()
 

The elliptic curves in class 33600gh have rank \(1\).

Complex multiplication

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

Modular form 33600.2.a.gh

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{7} + q^{9} - 4q^{11} - 2q^{13} + 6q^{17} + O(q^{20}) \)

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 Cremona 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 Cremona labels.