# Properties

 Label 18496e Number of curves $2$ Conductor $18496$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.s1")

sage: E.isogeny_class()

## Elliptic curves in class 18496e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.s2 18496e1 [0, -1, 0, -32753, -830479]  69632 $$\Gamma_0(N)$$-optimal
18496.s1 18496e2 [0, -1, 0, -425793, -106715455]  139264

## Rank

sage: E.rank()

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

## Modular form 18496.2.a.s

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. 