# Properties

 Label 7488.q Number of curves $2$ Conductor $7488$ CM no Rank $1$ Graph

# Related objects

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

E.isogeny_class()

## Elliptic curves in class 7488.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.q1 7488bc2 $$[0, 0, 0, -516, -3616]$$ $$5088448/1053$$ $$3144241152$$ $$[2]$$ $$4096$$ $$0.53758$$
7488.q2 7488bc1 $$[0, 0, 0, 69, -340]$$ $$778688/1521$$ $$-70963776$$ $$[2]$$ $$2048$$ $$0.19101$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7488.2.a.q

sage: E.q_eigenform(10)

$$q - 2 q^{5} + 2 q^{7} - 6 q^{11} + q^{13} + 2 q^{17} + 6 q^{19} + O(q^{20})$$

## 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.