# Properties

 Label 57330bt Number of curves $2$ Conductor $57330$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 57330bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
57330.h2 57330bt1 $$[1, -1, 0, 1755, -78975]$$ $$6967871/35100$$ $$-3010390847100$$ $$[2]$$ $$138240$$ $$1.0766$$ $$\Gamma_0(N)$$-optimal
57330.h1 57330bt2 $$[1, -1, 0, -20295, -991845]$$ $$10779215329/1232010$$ $$105664718733210$$ $$[2]$$ $$276480$$ $$1.4232$$

## Rank

sage: E.rank()

The elliptic curves in class 57330bt have rank $$0$$.

## Complex multiplication

The elliptic curves in class 57330bt do not have complex multiplication.

## Modular form 57330.2.a.bt

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} + q^{13} + q^{16} + 8q^{17} + 6q^{19} + O(q^{20})$$

## 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.