# Properties

 Label 21780n Number of curves $4$ Conductor $21780$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 21780n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
21780.l4 21780n1 [0, 0, 0, -49368, 4135417] [2] 103680 $$\Gamma_0(N)$$-optimal
21780.l3 21780n2 [0, 0, 0, -109263, -7855562] [2] 207360
21780.l2 21780n3 [0, 0, 0, -484968, -128352323] [2] 311040
21780.l1 21780n4 [0, 0, 0, -7732263, -8275761362] [2] 622080

## Rank

sage: E.rank()

The elliptic curves in class 21780n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 21780n do not have complex multiplication.

## Modular form 21780.2.a.n

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{7} + 4q^{13} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.