# Properties

 Label 18480.bc Number of curves $2$ Conductor $18480$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 18480.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18480.bc1 18480cb2 $$[0, -1, 0, -428645, 2042286477]$$ $$-2126464142970105856/438611057788643355$$ $$-1796550892702283182080$$ $$[]$$ $$1200000$$ $$2.7576$$
18480.bc2 18480cb1 $$[0, -1, 0, -143045, -24338643]$$ $$-79028701534867456/16987307596875$$ $$-69580011916800000$$ $$[]$$ $$240000$$ $$1.9529$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 18480.2.a.bc

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.