# Properties

 Label 7350.bo Number of curves $4$ Conductor $7350$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 7350.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bo1 7350bu3 [1, 1, 1, -457563, -119321469] [2] 73728
7350.bo2 7350bu2 [1, 1, 1, -28813, -1843969] [2, 2] 36864
7350.bo3 7350bu1 [1, 1, 1, -4313, 67031] [4] 18432 $$\Gamma_0(N)$$-optimal
7350.bo4 7350bu4 [1, 1, 1, 7937, -6180469] [2] 73728

## Rank

sage: E.rank()

The elliptic curves in class 7350.bo have rank $$1$$.

## Complex multiplication

The elliptic curves in class 7350.bo do not have complex multiplication.

## Modular form7350.2.a.bo

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} - 4q^{11} - q^{12} - 2q^{13} + q^{16} - 6q^{17} + q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.