# Properties

 Label 159120.dt Number of curves $4$ Conductor $159120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dt1")

sage: E.isogeny_class()

## Elliptic curves in class 159120.dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159120.dt1 159120dh4 $$[0, 0, 0, -294267, -61440694]$$ $$1887517194957938/21849165$$ $$32620628551680$$ $$$$ $$786432$$ $$1.7442$$
159120.dt2 159120dh2 $$[0, 0, 0, -18867, -907774]$$ $$994958062276/98903025$$ $$73830712550400$$ $$[2, 2]$$ $$393216$$ $$1.3976$$
159120.dt3 159120dh1 $$[0, 0, 0, -4287, 92414]$$ $$46689225424/7249905$$ $$1353006270720$$ $$$$ $$196608$$ $$1.0510$$ $$\Gamma_0(N)$$-optimal
159120.dt4 159120dh3 $$[0, 0, 0, 23253, -4386886]$$ $$931329171502/6107473125$$ $$-9118408515840000$$ $$$$ $$786432$$ $$1.7442$$

## Rank

sage: E.rank()

The elliptic curves in class 159120.dt have rank $$1$$.

## Complex multiplication

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

## Modular form 159120.2.a.dt

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{11} - q^{13} - q^{17} - 8q^{19} + O(q^{20})$$ ## 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. 