# Properties

 Label 18480.cz Number of curves $6$ Conductor $18480$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("18480.cz1")

sage: E.isogeny_class()

## Elliptic curves in class 18480.cz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
18480.cz1 18480df5 [0, 1, 0, -212000, 37498548] [4] 131072
18480.cz2 18480df3 [0, 1, 0, -14000, 512148] [2, 4] 65536
18480.cz3 18480df2 [0, 1, 0, -4320, -103500] [2, 2] 32768
18480.cz4 18480df1 [0, 1, 0, -4240, -107692] [2] 16384 $$\Gamma_0(N)$$-optimal
18480.cz5 18480df4 [0, 1, 0, 4080, -449580] [2] 65536
18480.cz6 18480df6 [0, 1, 0, 29120, 3082100] [4] 131072

## Rank

sage: E.rank()

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

## Modular form 18480.2.a.cz

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{7} + q^{9} - q^{11} - 2q^{13} + q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.