# Properties

 Label 18480.cj Number of curves 4 Conductor 18480 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18480.cj1")

sage: E.isogeny_class()

## Elliptic curves in class 18480.cj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18480.cj1 18480ct3 [0, 1, 0, -527856, -147786156]  147456
18480.cj2 18480ct2 [0, 1, 0, -33936, -2178540] [2, 2] 73728
18480.cj3 18480ct1 [0, 1, 0, -8016, 237204]  36864 $$\Gamma_0(N)$$-optimal
18480.cj4 18480ct4 [0, 1, 0, 45264, -10763820]  147456

## Rank

sage: E.rank()

The elliptic curves in class 18480.cj have rank $$1$$.

## Modular form 18480.2.a.cj

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + 2q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 