# Properties

 Label 46800dn Number of curves $2$ Conductor $46800$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dn1")

sage: E.isogeny_class()

## Elliptic curves in class 46800dn

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.f2 46800dn1 $$[0, 0, 0, -480, 3760]$$ $$163840/13$$ $$970444800$$ $$[]$$ $$25920$$ $$0.46803$$ $$\Gamma_0(N)$$-optimal
46800.f1 46800dn2 $$[0, 0, 0, -7680, -258320]$$ $$671088640/2197$$ $$164005171200$$ $$[]$$ $$77760$$ $$1.0173$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 46800.2.a.dn

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 