Properties

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

Related objects

Downloads

Learn more about

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

Elliptic curves in class 33600.gh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.gh1 33600gk4 \([0, 1, 0, -373633, 87780863]\) \(5633270409316/14175\) \(14515200000000\) \([2]\) \(196608\) \(1.7638\)  
33600.gh2 33600gk3 \([0, 1, 0, -65633, -4759137]\) \(30534944836/8203125\) \(8400000000000000\) \([2]\) \(196608\) \(1.7638\)  
33600.gh3 33600gk2 \([0, 1, 0, -23633, 1330863]\) \(5702413264/275625\) \(70560000000000\) \([2, 2]\) \(98304\) \(1.4172\)  
33600.gh4 33600gk1 \([0, 1, 0, 867, 81363]\) \(4499456/180075\) \(-2881200000000\) \([2]\) \(49152\) \(1.0706\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 33600.2.a.gh

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{7} + q^{9} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.