# Properties

 Label 142800ds Number of curves $2$ Conductor $142800$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ds1")

sage: E.isogeny_class()

## Elliptic curves in class 142800ds

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
142800.dh2 142800ds1 $$[0, -1, 0, 32592, -2714688]$$ $$59822347031/83966400$$ $$-5373849600000000$$ $$$$ $$663552$$ $$1.7040$$ $$\Gamma_0(N)$$-optimal
142800.dh1 142800ds2 $$[0, -1, 0, -207408, -26714688]$$ $$15417797707369/4080067320$$ $$261124308480000000$$ $$$$ $$1327104$$ $$2.0506$$

## Rank

sage: E.rank()

The elliptic curves in class 142800ds have rank $$1$$.

## Complex multiplication

The elliptic curves in class 142800ds do not have complex multiplication.

## Modular form 142800.2.a.ds

sage: E.q_eigenform(10)

$$q - q^{3} + q^{7} + q^{9} - 2q^{11} + 2q^{13} - q^{17} + 4q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 