# Properties

 Label 51600.dm Number of curves $2$ Conductor $51600$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 51600.dm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.dm1 51600dg2 $$[0, 1, 0, -893333, 324792963]$$ $$-1971080396800/715563$$ $$-28622520000000000$$ $$[]$$ $$440640$$ $$2.1263$$
51600.dm2 51600dg1 $$[0, 1, 0, 6667, 1692963]$$ $$819200/31347$$ $$-1253880000000000$$ $$[]$$ $$146880$$ $$1.5770$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 51600.dm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.dm do not have complex multiplication.

## Modular form 51600.2.a.dm

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.