# Properties

 Label 14490c Number of curves $2$ Conductor $14490$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 14490c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14490.k1 14490c1 $$[1, -1, 0, -44339415, 47524672925]$$ $$489781415227546051766883/233890092903563264000$$ $$4603658698620835725312000$$ $$$$ $$3096576$$ $$3.4263$$ $$\Gamma_0(N)$$-optimal
14490.k2 14490c2 $$[1, -1, 0, 159149865, 361345840541]$$ $$22649115256119592694355357/15973509811739648000000$$ $$-314406593624471491584000000$$ $$$$ $$6193152$$ $$3.7729$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 14490.2.a.c

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 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. 