# Properties

 Label 14490.ca Number of curves $2$ Conductor $14490$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ca1")

sage: E.isogeny_class()

## Elliptic curves in class 14490.ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.ca1 14490bi1 $$[1, -1, 1, -4926602, -1758530871]$$ $$489781415227546051766883/233890092903563264000$$ $$6315032508396208128000$$ $$[2]$$ $$1032192$$ $$2.8770$$ $$\Gamma_0(N)$$-optimal
14490.ca2 14490bi2 $$[1, -1, 1, 17683318, -13389073719]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-431284764916970496000000$$ $$[2]$$ $$2064384$$ $$3.2236$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 14490.2.a.ca

sage: E.q_eigenform(10)

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

## 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 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.