# Properties

 Label 3920.bg Number of curves $2$ Conductor $3920$ CM no Rank $1$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 3920.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.bg1 3920w2 $$[0, -1, 0, -19056, -1006144]$$ $$544737993463/20000$$ $$28098560000$$ $$$$ $$7680$$ $$1.0925$$
3920.bg2 3920w1 $$[0, -1, 0, -1136, -16960]$$ $$-115501303/25600$$ $$-35966156800$$ $$$$ $$3840$$ $$0.74595$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3920.bg have rank $$1$$.

## Complex multiplication

The elliptic curves in class 3920.bg do not have complex multiplication.

## Modular form3920.2.a.bg

sage: E.q_eigenform(10)

$$q + 2q^{3} - q^{5} + q^{9} + 4q^{11} - 2q^{13} - 2q^{15} - 8q^{17} - 6q^{19} + O(q^{20})$$ ## 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 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. 