# Properties

 Label 18496.k Number of curves $4$ Conductor $18496$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.k1")

sage: E.isogeny_class()

## Elliptic curves in class 18496.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.k1 18496j3 [0, 0, 0, -1677356, 836153296] [2] 147456
18496.k2 18496j2 [0, 0, 0, -105196, 12970320] [2, 2] 73728
18496.k3 18496j1 [0, 0, 0, -12716, -235824] [2] 36864 $$\Gamma_0(N)$$-optimal
18496.k4 18496j4 [0, 0, 0, -12716, 34980560] [2] 147456

## Rank

sage: E.rank()

The elliptic curves in class 18496.k have rank $$0$$.

## Modular form 18496.2.a.k

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.