# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("co1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.co

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.co1 51600dk1 $$[0, 1, 0, -808, -1612]$$ $$912673/516$$ $$33024000000$$ $$[2]$$ $$36864$$ $$0.70837$$ $$\Gamma_0(N)$$-optimal
51600.co2 51600dk2 $$[0, 1, 0, 3192, -9612]$$ $$56181887/33282$$ $$-2130048000000$$ $$[2]$$ $$73728$$ $$1.0549$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 51600.2.a.co

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} + 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.