# Properties

 Label 46800.p Number of curves $2$ Conductor $46800$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 46800.p

sage: E.isogeny_class().curves

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

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 46800.2.a.p

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 LMFDB 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 LMFDB labels. 