# Properties

 Label 882.i Number of curves $6$ Conductor $882$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("882.i1")

sage: E.isogeny_class()

## Elliptic curves in class 882.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
882.i1 882i6 [1, -1, 1, -1204160, -508296477] [2] 6912
882.i2 882i5 [1, -1, 1, -75200, -7941405] [2] 3456
882.i3 882i4 [1, -1, 1, -15665, -614631] [2] 2304
882.i4 882i2 [1, -1, 1, -4640, 122721] [2] 768
882.i5 882i1 [1, -1, 1, -230, 2769] [2] 384 $$\Gamma_0(N)$$-optimal
882.i6 882i3 [1, -1, 1, 1975, -57207] [2] 1152

## Rank

sage: E.rank()

The elliptic curves in class 882.i have rank $$0$$.

## Modular form882.2.a.i

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} + 4q^{13} + q^{16} + 6q^{17} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.