# Properties

 Label 18032ba Number of curves $2$ Conductor $18032$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ba1")

sage: E.isogeny_class()

## Elliptic curves in class 18032ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18032.v2 18032ba1 $$[0, -1, 0, 27032, 8037744]$$ $$4533086375/60669952$$ $$-29236261612945408$$ $$[2]$$ $$129024$$ $$1.8403$$ $$\Gamma_0(N)$$-optimal
18032.v1 18032ba2 $$[0, -1, 0, -474728, 118023536]$$ $$24553362849625/1755162752$$ $$845795912130756608$$ $$[2]$$ $$258048$$ $$2.1869$$

## Rank

sage: E.rank()

The elliptic curves in class 18032ba have rank $$0$$.

## Complex multiplication

The elliptic curves in class 18032ba do not have complex multiplication.

## Modular form 18032.2.a.ba

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{9} - 4q^{11} - 6q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.