# Properties

 Label 159936.gv Number of curves $6$ Conductor $159936$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("159936.gv1")

sage: E.isogeny_class()

## Elliptic curves in class 159936.gv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159936.gv1 159936s6 [0, 1, 0, -43021542209, -3434621350524225] [2] 283115520
159936.gv2 159936s4 [0, 1, 0, -2693962049, -53452178201409] [2, 2] 141557760
159936.gv3 159936s5 [0, 1, 0, -917606209, -122887441088833] [2] 283115520
159936.gv4 159936s2 [0, 1, 0, -284510529, 464118461631] [2, 2] 70778880
159936.gv5 159936s1 [0, 1, 0, -220285249, 1256774022335] [2] 35389440 $$\Gamma_0(N)$$-optimal
159936.gv6 159936s3 [0, 1, 0, 1097336511, 3651486844095] [2] 141557760

## Rank

sage: E.rank()

The elliptic curves in class 159936.gv have rank $$0$$.

## Modular form 159936.2.a.gv

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{13} - 2q^{15} - q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.