# Properties

 Label 880.j Number of curves 4 Conductor 880 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("880.j1")

sage: E.isogeny_class()

## Elliptic curves in class 880.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
880.j1 880j4 [0, -1, 0, -7100, 232652]  864
880.j2 880j3 [0, -1, 0, -445, 3720]  432
880.j3 880j2 [0, -1, 0, -100, 252]  288
880.j4 880j1 [0, -1, 0, -45, -100]  144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 880.j have rank $$0$$.

## Modular form880.2.a.j

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 