# Properties

 Label 20160be Number of curves $4$ Conductor $20160$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20160.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 20160be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.bj4 20160be1 [0, 0, 0, 1332, 29808]  24576 $$\Gamma_0(N)$$-optimal
20160.bj3 20160be2 [0, 0, 0, -10188, 320112] [2, 2] 49152
20160.bj2 20160be3 [0, 0, 0, -50508, -4082832]  98304
20160.bj1 20160be4 [0, 0, 0, -154188, 23302512]  98304

## Rank

sage: E.rank()

The elliptic curves in class 20160be have rank $$0$$.

## Modular form 20160.2.a.bj

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + 4q^{11} + 6q^{13} - 2q^{17} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 