# Properties

 Label 3864a Number of curves $2$ Conductor $3864$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("a1")

E.isogeny_class()

## Elliptic curves in class 3864a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3864.b2 3864a1 $$[0, -1, 0, -1568, -44100]$$ $$-416618810500/598934007$$ $$-613308423168$$ $$[2]$$ $$5376$$ $$0.95392$$ $$\Gamma_0(N)$$-optimal
3864.b1 3864a2 $$[0, -1, 0, -30728, -2061972]$$ $$1566789944863250/925924041$$ $$1896292435968$$ $$[2]$$ $$10752$$ $$1.3005$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3864.2.a.a

sage: E.q_eigenform(10)

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

## 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.