# Properties

 Label 46800do Number of curves $4$ Conductor $46800$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("do1")

sage: E.isogeny_class()

## Elliptic curves in class 46800do

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.d2 46800do1 $$[0, 0, 0, -117075, 15327250]$$ $$3803721481/26000$$ $$1213056000000000$$ $$[2]$$ $$331776$$ $$1.7283$$ $$\Gamma_0(N)$$-optimal
46800.d3 46800do2 $$[0, 0, 0, -45075, 33975250]$$ $$-217081801/10562500$$ $$-492804000000000000$$ $$[2]$$ $$663552$$ $$2.0749$$
46800.d1 46800do3 $$[0, 0, 0, -747075, -238562750]$$ $$988345570681/44994560$$ $$2099266191360000000$$ $$[2]$$ $$995328$$ $$2.2776$$
46800.d4 46800do4 $$[0, 0, 0, 404925, -907874750]$$ $$157376536199/7722894400$$ $$-360319361126400000000$$ $$[2]$$ $$1990656$$ $$2.6242$$

## Rank

sage: E.rank()

The elliptic curves in class 46800do have rank $$1$$.

## Complex multiplication

The elliptic curves in class 46800do do not have complex multiplication.

## Modular form 46800.2.a.do

sage: E.q_eigenform(10)

$$q - 4q^{7} - 6q^{11} - q^{13} - 6q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.