# Properties

 Label 470106.bj Number of curves 2 Conductor 470106 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("470106.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 470106.bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
470106.bj1 470106bj1 [1, -1, 0, -68710455, 219293910877] [] 50577408 $$\Gamma_0(N)$$-optimal
470106.bj2 470106bj2 [1, -1, 0, 381281535, -9679337330153] [] 354041856

## Rank

sage: E.rank()

The elliptic curves in class 470106.bj have rank $$0$$.

## Modular form 470106.2.a.bj

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 