# Properties

 Label 18496.j Number of curves $4$ Conductor $18496$ CM -4 Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.j1")

sage: E.isogeny_class()

## Elliptic curves in class 18496.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.j1 18496i3 [0, 0, 0, -12716, -550256] [2] 20480
18496.j2 18496i4 [0, 0, 0, -12716, 550256] [2] 20480
18496.j3 18496i2 [0, 0, 0, -1156, 0] [2, 2] 10240
18496.j4 18496i1 [0, 0, 0, 289, 0] [2] 5120 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 18496.j have rank $$2$$.

## Modular form 18496.2.a.j

sage: E.q_eigenform(10)

$$q - 2q^{5} - 3q^{9} - 6q^{13} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.