# Properties

 Label 880.e Number of curves $2$ Conductor $880$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

## Elliptic curves in class 880.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
880.e1 880a2 $$[0, 0, 0, -23, 38]$$ $$5256144/605$$ $$154880$$ $$[2]$$ $$64$$ $$-0.27207$$
880.e2 880a1 $$[0, 0, 0, 2, 3]$$ $$55296/275$$ $$-4400$$ $$[2]$$ $$32$$ $$-0.61864$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 880.e have rank $$1$$.

## Complex multiplication

The elliptic curves in class 880.e do not have complex multiplication.

## Modular form880.2.a.e

sage: E.q_eigenform(10)

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

## 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.