# Properties

 Label 18496.r Number of curves $2$ Conductor $18496$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.r1")

sage: E.isogeny_class()

## Elliptic curves in class 18496.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.r1 18496m2 [0, -1, 0, -1473, 22241] [2] 8192
18496.r2 18496m1 [0, -1, 0, -113, 209] [2] 4096 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 18496.2.a.r

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 LMFDB 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 LMFDB labels.