# Properties

 Label 14490.cb Number of curves $2$ Conductor $14490$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cb1")

sage: E.isogeny_class()

## Elliptic curves in class 14490.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.cb1 14490cb1 $$[1, -1, 1, -212, -601]$$ $$1439069689/579600$$ $$422528400$$ $$[2]$$ $$6144$$ $$0.35311$$ $$\Gamma_0(N)$$-optimal
14490.cb2 14490cb2 $$[1, -1, 1, 688, -4921]$$ $$49471280711/41992020$$ $$-30612182580$$ $$[2]$$ $$12288$$ $$0.69968$$

## Rank

sage: E.rank()

The elliptic curves in class 14490.cb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 14490.cb do not have complex multiplication.

## Modular form 14490.2.a.cb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 2q^{11} + 4q^{13} + q^{14} + q^{16} + 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.