# Properties

 Label 18496f Number of curves $2$ Conductor $18496$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.c1")

sage: E.isogeny_class()

## Elliptic curves in class 18496f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.c2 18496f1 [0, 1, 0, -113, -209] [2] 4096 $$\Gamma_0(N)$$-optimal
18496.c1 18496f2 [0, 1, 0, -1473, -22241] [2] 8192

## Rank

sage: E.rank()

The elliptic curves in class 18496f have rank $$1$$.

## Modular form 18496.2.a.c

sage: E.q_eigenform(10)

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

## 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 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.