# Properties

 Label 119952.bh Number of curves $6$ Conductor $119952$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 119952.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
119952.bh1 119952gt6 $$[0, 0, 0, -195761811, 1054241418706]$$ $$2361739090258884097/5202$$ $$1827452360466432$$ $$[2]$$ $$9437184$$ $$3.0625$$
119952.bh2 119952gt4 $$[0, 0, 0, -12235251, 16472132530]$$ $$576615941610337/27060804$$ $$9506407179146379264$$ $$[2, 2]$$ $$4718592$$ $$2.7159$$
119952.bh3 119952gt5 $$[0, 0, 0, -11600211, 18258246034]$$ $$-491411892194497/125563633938$$ $$-44110257444971374583808$$ $$[2]$$ $$9437184$$ $$3.0625$$
119952.bh4 119952gt2 $$[0, 0, 0, -804531, 229079410]$$ $$163936758817/30338064$$ $$10657702166240231424$$ $$[2, 2]$$ $$2359296$$ $$2.3693$$
119952.bh5 119952gt1 $$[0, 0, 0, -240051, -41983886]$$ $$4354703137/352512$$ $$123836771721019392$$ $$[2]$$ $$1179648$$ $$2.0228$$ $$\Gamma_0(N)$$-optimal
119952.bh6 119952gt3 $$[0, 0, 0, 1594509, 1334077234]$$ $$1276229915423/2927177028$$ $$-1028311528127972917248$$ $$[2]$$ $$4718592$$ $$2.7159$$

## Rank

sage: E.rank()

The elliptic curves in class 119952.bh have rank $$1$$.

## Complex multiplication

The elliptic curves in class 119952.bh do not have complex multiplication.

## Modular form 119952.2.a.bh

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.