# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 3920.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3920.p1 3920p2 [0, -1, 0, -25496, 1709296] [] 12096
3920.p2 3920p1 [0, -1, 0, 1944, -2960] [] 4032 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form3920.2.a.p

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.