# Properties

 Label 46200.dd Number of curves $2$ Conductor $46200$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dd1")

sage: E.isogeny_class()

## Elliptic curves in class 46200.dd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46200.dd1 46200dh2 $$[0, 1, 0, -1328, -17952]$$ $$1012523146/68607$$ $$17563392000$$ $$$$ $$36864$$ $$0.71443$$
46200.dd2 46200dh1 $$[0, 1, 0, 72, -1152]$$ $$318028/4851$$ $$-620928000$$ $$$$ $$18432$$ $$0.36785$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 46200.dd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 46200.dd do not have complex multiplication.

## Modular form 46200.2.a.dd

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} + q^{9} + q^{11} + 2 q^{13} - 6 q^{17} - 2 q^{19} + O(q^{20})$$

## 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. 