# Properties

 Label 3920.w Number of curves $2$ Conductor $3920$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("w1")

E.isogeny_class()

## Elliptic curves in class 3920.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3920.w1 3920be1 $$[0, 1, 0, -48820, 4138168]$$ $$-177953104/125$$ $$-9039207968000$$ $$[]$$ $$12096$$ $$1.4223$$ $$\Gamma_0(N)$$-optimal
3920.w2 3920be2 $$[0, 1, 0, 47220, 17660600]$$ $$161017136/1953125$$ $$-141237624500000000$$ $$[]$$ $$36288$$ $$1.9716$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3920.2.a.w

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.