# Properties

 Label 274890.cx Number of curves $2$ Conductor $274890$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cx1")

sage: E.isogeny_class()

## Elliptic curves in class 274890.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
274890.cx1 274890cx2 [1, 0, 1, -7033, -145582] [2] 737280
274890.cx2 274890cx1 [1, 0, 1, 1297, -15634] [2] 368640 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 274890.cx have rank $$1$$.

## Complex multiplication

The elliptic curves in class 274890.cx do not have complex multiplication.

## Modular form 274890.2.a.cx

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + q^{11} + q^{12} + q^{15} + q^{16} - q^{17} - q^{18} + O(q^{20})$$

## 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.