# Properties

 Label 159120.dr Number of curves $2$ Conductor $159120$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 159120.dr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.dr1 159120de1 $$[0, 0, 0, -2529147, 1545816314]$$ $$2396726313900986596/4154072495625$$ $$3100998501694080000$$ $$[2]$$ $$2949120$$ $$2.4421$$ $$\Gamma_0(N)$$-optimal
159120.dr2 159120de2 $$[0, 0, 0, -1738227, 2530195346]$$ $$-389032340685029858/1627263833203125$$ $$-2429491884861600000000$$ $$[2]$$ $$5898240$$ $$2.7886$$

## Rank

sage: E.rank()

The elliptic curves in class 159120.dr have rank $$0$$.

## Complex multiplication

The elliptic curves in class 159120.dr do not have complex multiplication.

## Modular form 159120.2.a.dr

sage: E.q_eigenform(10)

$$q + q^{5} + 2 q^{11} - q^{13} + q^{17} + 8 q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.