# Properties

 Label 58800.cu Number of curves $8$ Conductor $58800$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cu1")

sage: E.isogeny_class()

## Elliptic curves in class 58800.cu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.cu1 58800fc7 $$[0, -1, 0, -104537008, -411354663488]$$ $$16778985534208729/81000$$ $$609892416000000000$$ $$[2]$$ $$3981312$$ $$3.0350$$
58800.cu2 58800fc8 $$[0, -1, 0, -8889008, -1385383488]$$ $$10316097499609/5859375000$$ $$44118375000000000000000$$ $$[2]$$ $$3981312$$ $$3.0350$$
58800.cu3 58800fc6 $$[0, -1, 0, -6537008, -6418663488]$$ $$4102915888729/9000000$$ $$67765824000000000000$$ $$[2, 2]$$ $$1990656$$ $$2.6884$$
58800.cu4 58800fc5 $$[0, -1, 0, -5655008, 5177872512]$$ $$2656166199049/33750$$ $$254121840000000000$$ $$[2]$$ $$1327104$$ $$2.4857$$
58800.cu5 58800fc4 $$[0, -1, 0, -1343008, -515535488]$$ $$35578826569/5314410$$ $$40015041413760000000$$ $$[2]$$ $$1327104$$ $$2.4857$$
58800.cu6 58800fc2 $$[0, -1, 0, -363008, 76384512]$$ $$702595369/72900$$ $$548903174400000000$$ $$[2, 2]$$ $$663552$$ $$2.1391$$
58800.cu7 58800fc3 $$[0, -1, 0, -265008, -171751488]$$ $$-273359449/1536000$$ $$-11565367296000000000$$ $$[2]$$ $$995328$$ $$2.3418$$
58800.cu8 58800fc1 $$[0, -1, 0, 28992, 5824512]$$ $$357911/2160$$ $$-16263797760000000$$ $$[2]$$ $$331776$$ $$1.7925$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58800.cu have rank $$1$$.

## Complex multiplication

The elliptic curves in class 58800.cu do not have complex multiplication.

## Modular form 58800.2.a.cu

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} + 2q^{13} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 12 & 3 & 6 & 4 & 12 \\ 4 & 1 & 2 & 3 & 12 & 6 & 4 & 12 \\ 2 & 2 & 1 & 6 & 6 & 3 & 2 & 6 \\ 12 & 3 & 6 & 1 & 4 & 2 & 12 & 4 \\ 3 & 12 & 6 & 4 & 1 & 2 & 12 & 4 \\ 6 & 6 & 3 & 2 & 2 & 1 & 6 & 2 \\ 4 & 4 & 2 & 12 & 12 & 6 & 1 & 3 \\ 12 & 12 & 6 & 4 & 4 & 2 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.