# Properties

 Label 38962.bf Number of curves $2$ Conductor $38962$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 38962.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.bf1 38962w2 $$[1, 1, 1, -73268, -7176971]$$ $$24553362849625/1755162752$$ $$3109377880095872$$ $$$$ $$286720$$ $$1.7197$$
38962.bf2 38962w1 $$[1, 1, 1, 4172, -486155]$$ $$4533086375/60669952$$ $$-107480520835072$$ $$$$ $$143360$$ $$1.3731$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 38962.bf have rank $$1$$.

## Complex multiplication

The elliptic curves in class 38962.bf do not have complex multiplication.

## Modular form 38962.2.a.bf

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - q^{7} + q^{8} + q^{9} + 2q^{12} - q^{14} + q^{16} - 6q^{17} + q^{18} + 6q^{19} + O(q^{20})$$ ## 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 LMFDB 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 LMFDB labels. 