# Properties

 Label 101430.bp Number of curves $6$ Conductor $101430$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("101430.bp1")

sage: E.isogeny_class()

## Elliptic curves in class 101430.bp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
101430.bp1 101430co4 [1, -1, 0, -48686409, 130767600865] [2] 4718592
101430.bp2 101430co6 [1, -1, 0, -11391039, -12672659777] [2] 9437184
101430.bp3 101430co3 [1, -1, 0, -3122289, 1931606473] [2, 2] 4718592
101430.bp4 101430co2 [1, -1, 0, -3042909, 2043802165] [2, 2] 2359296
101430.bp5 101430co1 [1, -1, 0, -185229, 33710053] [2] 1179648 $$\Gamma_0(N)$$-optimal
101430.bp6 101430co5 [1, -1, 0, 3876381, 9354395875] [2] 9437184

## Rank

sage: E.rank()

The elliptic curves in class 101430.bp have rank $$1$$.

## Modular form 101430.2.a.bp

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4q^{11} + 2q^{13} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.