# Properties

 Label 159120.ek Number of curves 8 Conductor 159120 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("159120.ek1")

sage: E.isogeny_class()

## Elliptic curves in class 159120.ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159120.ek1 159120z8 [0, 0, 0, -949104000867, -355892486813447326] [2] 637009920
159120.ek2 159120z6 [0, 0, 0, -59319000867, -5560819946447326] [2, 2] 318504960
159120.ek3 159120z7 [0, 0, 0, -59211435747, -5581991709347614] [2] 637009920
159120.ek4 159120z5 [0, 0, 0, -11717750307, -488156229494494] [2] 212336640
159120.ek5 159120z3 [0, 0, 0, -3714161187, -86556842855134] [2] 159252480
159120.ek6 159120z2 [0, 0, 0, -800246307, -6128776387294] [2, 2] 106168320
159120.ek7 159120z1 [0, 0, 0, -301845027, 1943629784354] [2] 53084160 $$\Gamma_0(N)$$-optimal
159120.ek8 159120z4 [0, 0, 0, 2142837213, -40735318265566] [2] 212336640

## Rank

sage: E.rank()

The elliptic curves in class 159120.ek have rank $$1$$.

## Modular form 159120.2.a.ek

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} + q^{13} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.