# Properties

 Label 46800dm Number of curves $4$ Conductor $46800$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dm1")

sage: E.isogeny_class()

## Elliptic curves in class 46800dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
46800.s4 46800dm1 $$[0, 0, 0, 1725, -58750]$$ $$12167/39$$ $$-1819584000000$$ $$$$ $$65536$$ $$1.0357$$ $$\Gamma_0(N)$$-optimal
46800.s3 46800dm2 $$[0, 0, 0, -16275, -688750]$$ $$10218313/1521$$ $$70963776000000$$ $$[2, 2]$$ $$131072$$ $$1.3822$$
46800.s2 46800dm3 $$[0, 0, 0, -70275, 6493250]$$ $$822656953/85683$$ $$3997626048000000$$ $$$$ $$262144$$ $$1.7288$$
46800.s1 46800dm4 $$[0, 0, 0, -250275, -48190750]$$ $$37159393753/1053$$ $$49128768000000$$ $$$$ $$262144$$ $$1.7288$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 46800.2.a.dm

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 