# Properties

 Label 141120eq Number of curves $4$ Conductor $141120$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("eq1")

sage: E.isogeny_class()

## Elliptic curves in class 141120eq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
141120.hh3 141120eq1 $$[0, 0, 0, -16023, -389648]$$ $$82881856/36015$$ $$197687478260160$$ $$$$ $$589824$$ $$1.4393$$ $$\Gamma_0(N)$$-optimal
141120.hh2 141120eq2 $$[0, 0, 0, -124068, 16551808]$$ $$601211584/11025$$ $$3873060798566400$$ $$[2, 2]$$ $$1179648$$ $$1.7858$$
141120.hh1 141120eq3 $$[0, 0, 0, -1976268, 1069342288]$$ $$303735479048/105$$ $$295090346557440$$ $$$$ $$2359296$$ $$2.1324$$
141120.hh4 141120eq4 $$[0, 0, 0, -588, 48014512]$$ $$-8/354375$$ $$-995929919631360000$$ $$$$ $$2359296$$ $$2.1324$$

## Rank

sage: E.rank()

The elliptic curves in class 141120eq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 141120eq do not have complex multiplication.

## Modular form 141120.2.a.eq

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{11} + 6q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$ ## 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 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. 