# Properties

 Label 162288.dr Number of curves $2$ Conductor $162288$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dr1")

sage: E.isogeny_class()

## Elliptic curves in class 162288.dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162288.dr1 162288bp2 $$[0, 0, 0, -4272555, -3182362918]$$ $$24553362849625/1755162752$$ $$616585219943321567232$$ $$$$ $$6193152$$ $$2.7362$$
162288.dr2 162288bp1 $$[0, 0, 0, 243285, -217262374]$$ $$4533086375/60669952$$ $$-21313234715837202432$$ $$$$ $$3096576$$ $$2.3896$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 162288.dr have rank $$0$$.

## Complex multiplication

The elliptic curves in class 162288.dr do not have complex multiplication.

## Modular form 162288.2.a.dr

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 