# Properties

 Label 3864d Number of curves $2$ Conductor $3864$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 3864d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3864.e2 3864d1 $$[0, 1, 0, 128, -592]$$ $$224727548/299943$$ $$-307141632$$ $$$$ $$1280$$ $$0.31437$$ $$\Gamma_0(N)$$-optimal
3864.e1 3864d2 $$[0, 1, 0, -792, -6480]$$ $$26860713266/7394247$$ $$15143417856$$ $$$$ $$2560$$ $$0.66095$$

## Rank

sage: E.rank()

The elliptic curves in class 3864d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 3864d do not have complex multiplication.

## Modular form3864.2.a.d

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels. 