# Properties

 Label 338130p Number of curves $2$ Conductor $338130$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 338130p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.p2 338130p1 [1, -1, 0, -8649524115, -266718851520075] [2] 601620480 $$\Gamma_0(N)$$-optimal
338130.p1 338130p2 [1, -1, 0, -132994802835, -18667606756118859] [2] 1203240960

## Rank

sage: E.rank()

The elliptic curves in class 338130p have rank $$0$$.

## Complex multiplication

The elliptic curves in class 338130p do not have complex multiplication.

## Modular form 338130.2.a.p

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - q^{13} + q^{16} + O(q^{20})$$

## 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.