# Properties

 Label 41280.bu Number of curves $4$ Conductor $41280$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bu1")

sage: E.isogeny_class()

## Elliptic curves in class 41280.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41280.bu1 41280u4 $$[0, -1, 0, -53665, 4770337]$$ $$65202655558249/512820150$$ $$134432725401600$$ $$[4]$$ $$147456$$ $$1.5392$$
41280.bu2 41280u2 $$[0, -1, 0, -5665, -39263]$$ $$76711450249/41602500$$ $$10905845760000$$ $$[2, 2]$$ $$73728$$ $$1.1926$$
41280.bu3 41280u1 $$[0, -1, 0, -4385, -110175]$$ $$35578826569/51600$$ $$13526630400$$ $$[2]$$ $$36864$$ $$0.84606$$ $$\Gamma_0(N)$$-optimal
41280.bu4 41280u3 $$[0, -1, 0, 21855, -330975]$$ $$4403686064471/2721093750$$ $$-713318400000000$$ $$[2]$$ $$147456$$ $$1.5392$$

## Rank

sage: E.rank()

The elliptic curves in class 41280.bu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 41280.bu do not have complex multiplication.

## Modular form 41280.2.a.bu

sage: E.q_eigenform(10)

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

## 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.