# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.l1")

sage: E.isogeny_class()

## Elliptic curves in class 18496b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.l1 18496b1 [0, 0, 0, -5780, -157216] [2] 18432 $$\Gamma_0(N)$$-optimal
18496.l2 18496b2 [0, 0, 0, 5780, -707472] [2] 36864

## Rank

sage: E.rank()

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

## Modular form 18496.2.a.l

sage: E.q_eigenform(10)

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

## 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.