# Properties

 Label 162240.fl Number of curves $4$ Conductor $162240$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("fl1")

sage: E.isogeny_class()

## Elliptic curves in class 162240.fl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162240.fl1 162240gi4 $$[0, 1, 0, -146241, -17555745]$$ $$2186875592/428415$$ $$67760205913620480$$ $$[2]$$ $$1032192$$ $$1.9463$$
162240.fl2 162240gi2 $$[0, 1, 0, -44841, 3393495]$$ $$504358336/38025$$ $$751777432473600$$ $$[2, 2]$$ $$516096$$ $$1.5997$$
162240.fl3 162240gi1 $$[0, 1, 0, -43996, 3537314]$$ $$30488290624/195$$ $$60238576320$$ $$[2]$$ $$258048$$ $$1.2531$$ $$\Gamma_0(N)$$-optimal
162240.fl4 162240gi3 $$[0, 1, 0, 43039, 15151839]$$ $$55742968/658125$$ $$-104092259880960000$$ $$[2]$$ $$1032192$$ $$1.9463$$

## Rank

sage: E.rank()

The elliptic curves in class 162240.fl have rank $$0$$.

## Complex multiplication

The elliptic curves in class 162240.fl do not have complex multiplication.

## Modular form 162240.2.a.fl

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} - q^{15} + 2 q^{17} - 4 q^{19} + O(q^{20})$$

## 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.