# Properties

 Label 14490.by Number of curves $4$ Conductor $14490$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 14490.by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.by1 14490ca4 $$[1, -1, 1, -27131927, -142442449]$$ $$3029968325354577848895529/1753440696000000000000$$ $$1278258267384000000000000$$ $$[6]$$ $$2211840$$ $$3.3151$$
14490.by2 14490ca2 $$[1, -1, 1, -18664592, -31031884141]$$ $$986396822567235411402169/6336721794060000$$ $$4619470187869740000$$ $$[2]$$ $$737280$$ $$2.7658$$
14490.by3 14490ca1 $$[1, -1, 1, -1144112, -504199789]$$ $$-227196402372228188089/19338934824115200$$ $$-14098083486779980800$$ $$[2]$$ $$368640$$ $$2.4192$$ $$\Gamma_0(N)$$-optimal
14490.by4 14490ca3 $$[1, -1, 1, 6782953, -20348881]$$ $$47342661265381757089751/27397579603968000000$$ $$-19972835531292672000000$$ $$[6]$$ $$1105920$$ $$2.9685$$

## Rank

sage: E.rank()

The elliptic curves in class 14490.by have rank $$1$$.

## Complex multiplication

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

## Modular form 14490.2.a.by

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.