# Properties

 Label 7488.z Number of curves $2$ Conductor $7488$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 7488.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.z1 7488bq2 $$[0, 0, 0, -3540, -35584]$$ $$1643032000/767637$$ $$2292151799808$$ $$$$ $$10240$$ $$1.0661$$
7488.z2 7488bq1 $$[0, 0, 0, -2955, -61792]$$ $$61162984000/41067$$ $$1916021952$$ $$$$ $$5120$$ $$0.71954$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 7488.z have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7488.z do not have complex multiplication.

## Modular form7488.2.a.z

sage: E.q_eigenform(10)

$$q - 2q^{7} - 4q^{11} - q^{13} + 6q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 