# Properties

 Label 21780.l Number of curves $4$ Conductor $21780$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("l1")

sage: E.isogeny_class()

## Elliptic curves in class 21780.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21780.l1 21780n4 $$[0, 0, 0, -7732263, -8275761362]$$ $$154639330142416/33275$$ $$11001240747129600$$ $$$$ $$622080$$ $$2.4627$$
21780.l2 21780n3 $$[0, 0, 0, -484968, -128352323]$$ $$610462990336/8857805$$ $$183033142930368720$$ $$$$ $$311040$$ $$2.1161$$
21780.l3 21780n2 $$[0, 0, 0, -109263, -7855562]$$ $$436334416/171875$$ $$56824590636000000$$ $$$$ $$207360$$ $$1.9134$$
21780.l4 21780n1 $$[0, 0, 0, -49368, 4135417]$$ $$643956736/15125$$ $$312535248498000$$ $$$$ $$103680$$ $$1.5668$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 21780.2.a.l

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 LMFDB 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 LMFDB labels. 