# Properties

 Label 18480cs Number of curves $2$ Conductor $18480$ CM no Rank $0$ Graph

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("cs1")

sage: E.isogeny_class()

## Elliptic curves in class 18480cs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.cd2 18480cs1 $$[0, 1, 0, -21, -126]$$ $$-67108864/343035$$ $$-5488560$$ $$[2]$$ $$3840$$ $$-0.022504$$ $$\Gamma_0(N)$$-optimal
18480.cd1 18480cs2 $$[0, 1, 0, -516, -4680]$$ $$59466754384/121275$$ $$31046400$$ $$[2]$$ $$7680$$ $$0.32407$$

## Rank

sage: E.rank()

The elliptic curves in class 18480cs have rank $$0$$.

## Complex multiplication

The elliptic curves in class 18480cs do not have complex multiplication.

## Modular form 18480.2.a.cs

sage: E.q_eigenform(10)

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

## 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.