# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bo1")

sage: E.isogeny_class()

## Elliptic curves in class 7488.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7488.bo1 7488ba2 $$[0, 0, 0, -104484, -12995552]$$ $$42246001231552/14414517$$ $$43041517129728$$ $$[2]$$ $$24576$$ $$1.5877$$
7488.bo2 7488ba1 $$[0, 0, 0, -5619, -261740]$$ $$-420526439488/390971529$$ $$-18241167657024$$ $$[2]$$ $$12288$$ $$1.2411$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form7488.2.a.bo

sage: E.q_eigenform(10)

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

## 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.