# Properties

 Label 159120.bh Number of curves $6$ Conductor $159120$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 159120.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.bh1 159120dz6 $$[0, 0, 0, -1750323, -884420782]$$ $$397210600760070242/3536192675535$$ $$5279507375032350720$$ $$[2]$$ $$2883584$$ $$2.4157$$
159120.bh2 159120dz4 $$[0, 0, 0, -189723, 9178778]$$ $$1011710313226084/536724738225$$ $$400662870186009600$$ $$[2, 2]$$ $$1441792$$ $$2.0691$$
159120.bh3 159120dz2 $$[0, 0, 0, -149223, 22163078]$$ $$1969080716416336/2472575625$$ $$461441953440000$$ $$[2, 2]$$ $$720896$$ $$1.7225$$
159120.bh4 159120dz1 $$[0, 0, 0, -149178, 22177127]$$ $$31476797652269056/49725$$ $$579992400$$ $$[2]$$ $$360448$$ $$1.3760$$ $$\Gamma_0(N)$$-optimal
159120.bh5 159120dz3 $$[0, 0, 0, -109443, 34248242]$$ $$-194204905090564/566398828125$$ $$-422814459600000000$$ $$[2]$$ $$1441792$$ $$2.0691$$
159120.bh6 159120dz5 $$[0, 0, 0, 722877, 71783138]$$ $$27980756504588158/17683545112935$$ $$-26401391385251051520$$ $$[2]$$ $$2883584$$ $$2.4157$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 159120.bh do not have complex multiplication.

## Modular form 159120.2.a.bh

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.