# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("159936.bb1")

sage: E.isogeny_class()

## Elliptic curves in class 159936in

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159936.bb5 159936in1 [0, -1, 0, -220285249, -1256774022335] [2] 35389440 $$\Gamma_0(N)$$-optimal
159936.bb4 159936in2 [0, -1, 0, -284510529, -464118461631] [2, 2] 70778880
159936.bb2 159936in3 [0, -1, 0, -2693962049, 53452178201409] [2, 2] 141557760
159936.bb6 159936in4 [0, -1, 0, 1097336511, -3651486844095] [2] 141557760
159936.bb1 159936in5 [0, -1, 0, -43021542209, 3434621350524225] [2] 283115520
159936.bb3 159936in6 [0, -1, 0, -917606209, 122887441088833] [2] 283115520

## Rank

sage: E.rank()

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

## Modular form 159936.2.a.bb

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 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.