# Properties

 Label 51600.du Number of curves $4$ Conductor $51600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("du1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.du

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.du1 51600w4 $$[0, 1, 0, -6495408, -6373780812]$$ $$947094050118111698/20769216075$$ $$664614914400000000$$ $$[2]$$ $$1966080$$ $$2.5356$$
51600.du2 51600w2 $$[0, 1, 0, -420408, -92230812]$$ $$513591322675396/68238500625$$ $$1091816010000000000$$ $$[2, 2]$$ $$983040$$ $$2.1890$$
51600.du3 51600w1 $$[0, 1, 0, -107908, 12144188]$$ $$34739908901584/4081640625$$ $$16326562500000000$$ $$[2]$$ $$491520$$ $$1.8424$$ $$\Gamma_0(N)$$-optimal
51600.du4 51600w3 $$[0, 1, 0, 654592, -485680812]$$ $$969360123836302/3748293231075$$ $$-119945383394400000000$$ $$[2]$$ $$1966080$$ $$2.5356$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 51600.2.a.du

sage: E.q_eigenform(10)

$$q + q^{3} + 4q^{7} + q^{9} - 6q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.