# Properties

 Label 33488.q Number of curves $2$ Conductor $33488$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 33488.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33488.q1 33488z2 $$[0, 0, 0, -335, -198]$$ $$16241202000/9332687$$ $$2389167872$$ $$$$ $$11520$$ $$0.48914$$
33488.q2 33488z1 $$[0, 0, 0, -220, 1251]$$ $$73598976000/336973$$ $$5391568$$ $$$$ $$5760$$ $$0.14257$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 33488.q have rank $$0$$.

## Complex multiplication

The elliptic curves in class 33488.q do not have complex multiplication.

## Modular form 33488.2.a.q

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 