# Properties

 Label 159936.bc Number of curves $4$ Conductor $159936$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 159936.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159936.bc1 159936cz4 $$[0, -1, 0, -106689, -12154911]$$ $$17418812548/1753941$$ $$13523314587009024$$ $$$$ $$983040$$ $$1.8314$$
159936.bc2 159936cz2 $$[0, -1, 0, -24369, 1263249]$$ $$830321872/127449$$ $$245665749417984$$ $$[2, 2]$$ $$491520$$ $$1.4848$$
159936.bc3 159936cz1 $$[0, -1, 0, -23389, 1384573]$$ $$11745974272/357$$ $$43008709632$$ $$$$ $$245760$$ $$1.1383$$ $$\Gamma_0(N)$$-optimal
159936.bc4 159936cz3 $$[0, -1, 0, 42271, 6900993]$$ $$1083360092/3306177$$ $$-25491434233724928$$ $$$$ $$983040$$ $$1.8314$$

## Rank

sage: E.rank()

The elliptic curves in class 159936.bc have rank $$1$$.

## Complex multiplication

The elliptic curves in class 159936.bc do not have complex multiplication.

## Modular form 159936.2.a.bc

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{9} - 4q^{11} + 6q^{13} + 2q^{15} - q^{17} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 