# Properties

 Label 38640.o Number of curves $4$ Conductor $38640$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 38640.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.o1 38640bf4 $$[0, -1, 0, -68696, -6907344]$$ $$8753151307882969/65205$$ $$267079680$$ $$[2]$$ $$90112$$ $$1.2115$$
38640.o2 38640bf2 $$[0, -1, 0, -4296, -106704]$$ $$2141202151369/5832225$$ $$23888793600$$ $$[2, 2]$$ $$45056$$ $$0.86491$$
38640.o3 38640bf3 $$[0, -1, 0, -2616, -192720]$$ $$-483551781049/3672913125$$ $$-15044252160000$$ $$[2]$$ $$90112$$ $$1.2115$$
38640.o4 38640bf1 $$[0, -1, 0, -376, -80]$$ $$1439069689/828345$$ $$3392901120$$ $$[2]$$ $$22528$$ $$0.51833$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 38640.2.a.o

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.