# Properties

 Label 18496k Number of curves $2$ Conductor $18496$ CM -4 Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.n1")

sage: E.isogeny_class()

## Elliptic curves in class 18496k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.n2 18496k1 [0, 0, 0, 17, 0] [2] 2048 $$\Gamma_0(N)$$-optimal
18496.n1 18496k2 [0, 0, 0, -68, 0] [2] 4096

## Rank

sage: E.rank()

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

## Modular form 18496.2.a.n

sage: E.q_eigenform(10)

$$q + 4q^{5} - 3q^{9} + 6q^{13} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.