# Properties

 Label 333795a Number of curves $2$ Conductor $333795$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 333795a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
333795.a2 333795a1 [0, -1, 1, -2583756, 1872892712] [] 26400000 $$\Gamma_0(N)$$-optimal
333795.a1 333795a2 [0, -1, 1, -7742406, -156763848628] [] 132000000

## Rank

sage: E.rank()

The elliptic curves in class 333795a have rank $$1$$.

## Complex multiplication

The elliptic curves in class 333795a do not have complex multiplication.

## Modular form 333795.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{2} - q^{3} + 2q^{4} - q^{5} + 2q^{6} - q^{7} + q^{9} + 2q^{10} - q^{11} - 2q^{12} - 6q^{13} + 2q^{14} + q^{15} - 4q^{16} - 2q^{18} - 5q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.