# Properties

 Label 33600.gh Number of curves $4$ Conductor $33600$ CM no Rank $0$ Graph # 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 $$[0, 1, 0, -373633, 87780863]$$ $$5633270409316/14175$$ $$14515200000000$$ $$$$ $$196608$$ $$1.7638$$
33600.gh2 33600gk3 $$[0, 1, 0, -65633, -4759137]$$ $$30534944836/8203125$$ $$8400000000000000$$ $$$$ $$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$$ $$$$ $$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)

$$q + q^{3} + q^{7} + q^{9} - 2q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$ ## 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. 