# Properties

 Label 235200.bg Number of curves $4$ Conductor $235200$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 235200.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.bg1 235200bg4 $$[0, -1, 0, -5489633, -4948828863]$$ $$303735479048/105$$ $$6324810240000000$$ $$[2]$$ $$7077888$$ $$2.3878$$
235200.bg2 235200bg2 $$[0, -1, 0, -344633, -76513863]$$ $$601211584/11025$$ $$83013134400000000$$ $$[2, 2]$$ $$3538944$$ $$2.0413$$
235200.bg3 235200bg1 $$[0, -1, 0, -44508, 1818762]$$ $$82881856/36015$$ $$4237128735000000$$ $$[2]$$ $$1769472$$ $$1.6947$$ $$\Gamma_0(N)$$-optimal
235200.bg4 235200bg3 $$[0, -1, 0, -1633, -222288863]$$ $$-8/354375$$ $$-21346234560000000000$$ $$[2]$$ $$7077888$$ $$2.3878$$

## Rank

sage: E.rank()

The elliptic curves in class 235200.bg have rank $$1$$.

## Complex multiplication

The elliptic curves in class 235200.bg do not have complex multiplication.

## Modular form 235200.2.a.bg

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} - 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.