# Properties

 Label 4800.u Number of curves $4$ Conductor $4800$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 4800.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4800.u1 4800bh3 $$[0, -1, 0, -5633, 163137]$$ $$38614472/405$$ $$207360000000$$ $$[2]$$ $$6144$$ $$0.98802$$
4800.u2 4800bh2 $$[0, -1, 0, -633, -1863]$$ $$438976/225$$ $$14400000000$$ $$[2, 2]$$ $$3072$$ $$0.64145$$
4800.u3 4800bh1 $$[0, -1, 0, -508, -4238]$$ $$14526784/15$$ $$15000000$$ $$[2]$$ $$1536$$ $$0.29488$$ $$\Gamma_0(N)$$-optimal
4800.u4 4800bh4 $$[0, -1, 0, 2367, -16863]$$ $$2863288/1875$$ $$-960000000000$$ $$[2]$$ $$6144$$ $$0.98802$$

## Rank

sage: E.rank()

The elliptic curves in class 4800.u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4800.u do not have complex multiplication.

## Modular form4800.2.a.u

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 4q^{11} + 2q^{13} + 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.