# Properties

 Label 38640.bo Number of curves $2$ Conductor $38640$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 38640.bo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.bo1 38640bz2 $$[0, -1, 0, -1075760, -423182400]$$ $$33613237452390629041/532385784000000$$ $$2180652171264000000$$ $$$$ $$829440$$ $$2.3192$$
38640.bo2 38640bz1 $$[0, -1, 0, -133680, 8667072]$$ $$64500981545311921/29485596672000$$ $$120773003968512000$$ $$$$ $$414720$$ $$1.9726$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 38640.bo have rank $$0$$.

## Complex multiplication

The elliptic curves in class 38640.bo do not have complex multiplication.

## Modular form 38640.2.a.bo

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} + 2q^{11} - 6q^{13} - q^{15} - 4q^{17} + 6q^{19} + O(q^{20})$$ ## 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. 