# Properties

 Label 14450.a Number of curves 4 Conductor 14450 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("14450.a1")

sage: E.isogeny_class()

## Elliptic curves in class 14450.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
14450.a1 14450g4 [1, 0, 1, -816576, -196331452]  497664
14450.a2 14450g3 [1, 0, 1, -744326, -247195452]  248832
14450.a3 14450g2 [1, 0, 1, -310826, 66658548]  165888
14450.a4 14450g1 [1, 0, 1, -21826, 766548]  82944 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 14450.a have rank $$1$$.

## Modular form 14450.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - 4q^{7} - q^{8} + q^{9} - 6q^{11} - 2q^{12} - 2q^{13} + 4q^{14} + q^{16} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 