# Properties

 Label 338130bp Number of curves $6$ Conductor $338130$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("338130.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 338130bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
338130.bp6 338130bp1 [1, -1, 0, 38961, -1195155] [2] 2359296 $$\Gamma_0(N)$$-optimal
338130.bp5 338130bp2 [1, -1, 0, -169119, -9809667] [2, 2] 4718592
338130.bp3 338130bp3 [1, -1, 0, -1469619, 679195233] [2, 2] 9437184
338130.bp2 338130bp4 [1, -1, 0, -2197899, -1252640295] [2] 9437184
338130.bp1 338130bp5 [1, -1, 0, -23448069, 43708604643] [2] 18874368
338130.bp4 338130bp6 [1, -1, 0, -299169, 1730493423] [2] 18874368

## Rank

sage: E.rank()

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

## Modular form 338130.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 4q^{11} + q^{13} + q^{16} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.