# Properties

 Label 4864.i Number of curves $2$ Conductor $4864$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 4864.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4864.i1 4864m2 $$[0, 0, 0, -200, 1088]$$ $$27000000/19$$ $$622592$$ $$[2]$$ $$576$$ $$0.047963$$
4864.i2 4864m1 $$[0, 0, 0, -10, 24]$$ $$-216000/361$$ $$-184832$$ $$[2]$$ $$288$$ $$-0.29861$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4864.i have rank $$1$$.

## Complex multiplication

The elliptic curves in class 4864.i do not have complex multiplication.

## Modular form4864.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.