# Properties

 Label 46800ek Number of curves $2$ Conductor $46800$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ek1")

sage: E.isogeny_class()

## Elliptic curves in class 46800ek

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.p1 46800ek1 $$[0, 0, 0, -3675, 18250]$$ $$117649/65$$ $$3032640000000$$ $$[2]$$ $$73728$$ $$1.0856$$ $$\Gamma_0(N)$$-optimal
46800.p2 46800ek2 $$[0, 0, 0, 14325, 144250]$$ $$6967871/4225$$ $$-197121600000000$$ $$[2]$$ $$147456$$ $$1.4321$$

## Rank

sage: E.rank()

The elliptic curves in class 46800ek have rank $$0$$.

## Complex multiplication

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

## Modular form 46800.2.a.ek

sage: E.q_eigenform(10)

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

## 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.