# Properties

 Label 254898.da Number of curves $4$ Conductor $254898$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 254898.da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
254898.da1 254898da3 $$[1, -1, 0, -647316126, 6339188682364]$$ $$14489843500598257/6246072$$ $$12930528707587828843128$$ $$[2]$$ $$84934656$$ $$3.5854$$
254898.da2 254898da4 $$[1, -1, 0, -86540526, -163771132820]$$ $$34623662831857/14438442312$$ $$29890256277572013807210888$$ $$[2]$$ $$84934656$$ $$3.5854$$
254898.da3 254898da2 $$[1, -1, 0, -40658886, 98020328692]$$ $$3590714269297/73410624$$ $$151973621353377938995776$$ $$[2, 2]$$ $$42467328$$ $$3.2388$$
254898.da4 254898da1 $$[1, -1, 0, 124794, 4584917812]$$ $$103823/4386816$$ $$-9081523591611753590784$$ $$[2]$$ $$21233664$$ $$2.8923$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 254898.da have rank $$1$$.

## Complex multiplication

The elliptic curves in class 254898.da do not have complex multiplication.

## Modular form 254898.2.a.da

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + 2q^{5} - q^{8} - 2q^{10} + 6q^{13} + q^{16} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.