# Properties

 Label 21160.e Number of curves 4 Conductor 21160 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("21160.e1")

sage: E.isogeny_class()

## Elliptic curves in class 21160.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
21160.e1 21160c4 [0, 0, 0, -56603, 5183142] [2] 49280
21160.e2 21160c2 [0, 0, 0, -3703, 73002] [2, 2] 24640
21160.e3 21160c1 [0, 0, 0, -1058, -12167] [2] 12320 $$\Gamma_0(N)$$-optimal
21160.e4 21160c3 [0, 0, 0, 6877, 413678] [2] 49280

## Rank

sage: E.rank()

The elliptic curves in class 21160.e have rank $$0$$.

## Modular form 21160.2.a.e

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} - 3q^{9} - 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.