# Properties

 Label 235200bal Number of curves $4$ Conductor $235200$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bal1")

sage: E.isogeny_class()

## Elliptic curves in class 235200bal

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235200.bal3 235200bal1 $$[0, 1, 0, -44508, -1818762]$$ $$82881856/36015$$ $$4237128735000000$$ $$[2]$$ $$1769472$$ $$1.6947$$ $$\Gamma_0(N)$$-optimal
235200.bal2 235200bal2 $$[0, 1, 0, -344633, 76513863]$$ $$601211584/11025$$ $$83013134400000000$$ $$[2, 2]$$ $$3538944$$ $$2.0413$$
235200.bal1 235200bal3 $$[0, 1, 0, -5489633, 4948828863]$$ $$303735479048/105$$ $$6324810240000000$$ $$[2]$$ $$7077888$$ $$2.3878$$
235200.bal4 235200bal4 $$[0, 1, 0, -1633, 222288863]$$ $$-8/354375$$ $$-21346234560000000000$$ $$[2]$$ $$7077888$$ $$2.3878$$

## Rank

sage: E.rank()

The elliptic curves in class 235200bal have rank $$2$$.

## Complex multiplication

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

## Modular form 235200.2.a.bal

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 Cremona 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 Cremona labels.