# Properties

 Label 18496g Number of curves 4 Conductor 18496 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18496.e1")

sage: E.isogeny_class()

## Elliptic curves in class 18496g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18496.e4 18496g1 [0, 1, 0, -55873, 3128607] [2] 110592 $$\Gamma_0(N)$$-optimal
18496.e3 18496g2 [0, 1, 0, -795713, 272874271] [2] 221184
18496.e2 18496g3 [0, 1, 0, -1905473, -1012893665] [2] 331776
18496.e1 18496g4 [0, 1, 0, -2090433, -804591713] [2] 663552

## Rank

sage: E.rank()

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

## Modular form 18496.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} + 4q^{7} + q^{9} + 6q^{11} - 2q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.