# Properties

 Label 3920.bd Number of curves $2$ Conductor $3920$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.bd1 3920g2 $$[0, -1, 0, -11776, 353760]$$ $$2185454/625$$ $$51652616960000$$ $$$$ $$10752$$ $$1.3379$$
3920.bd2 3920g1 $$[0, -1, 0, 1944, 35456]$$ $$19652/25$$ $$-1033052339200$$ $$$$ $$5376$$ $$0.99128$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 3920.bd have rank $$0$$.

## Complex multiplication

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

## Modular form3920.2.a.bd

sage: E.q_eigenform(10)

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