# Properties

 Label 8880.n Number of curves $4$ Conductor $8880$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 8880.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8880.n1 8880s4 $$[0, -1, 0, -167800, 11865712]$$ $$127568139540190201/59114336463360$$ $$242132322153922560$$ $$[2]$$ $$145152$$ $$2.0303$$
8880.n2 8880s2 $$[0, -1, 0, -85000, -9509648]$$ $$16581570075765001/998001000$$ $$4087812096000$$ $$[2]$$ $$48384$$ $$1.4810$$
8880.n3 8880s1 $$[0, -1, 0, -5000, -165648]$$ $$-3375675045001/999000000$$ $$-4091904000000$$ $$[2]$$ $$24192$$ $$1.1344$$ $$\Gamma_0(N)$$-optimal
8880.n4 8880s3 $$[0, -1, 0, 37000, 1379952]$$ $$1367594037332999/995878502400$$ $$-4079118345830400$$ $$[2]$$ $$72576$$ $$1.6837$$

## Rank

sage: E.rank()

The elliptic curves in class 8880.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 8880.n do not have complex multiplication.

## Modular form8880.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 4q^{7} + q^{9} - 6q^{11} + 2q^{13} - q^{15} - 6q^{17} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.