# Properties

 Label 54450fr Number of curves 4 Conductor 54450 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54450.gf1")

sage: E.isogeny_class()

## Elliptic curves in class 54450fr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54450.gf3 54450fr1 [1, -1, 1, -150305, 21193197] [2] 552960 $$\Gamma_0(N)$$-optimal
54450.gf4 54450fr2 [1, -1, 1, 121945, 89255697] [2] 1105920
54450.gf1 54450fr3 [1, -1, 1, -2192180, -1243952553] [2] 1658880
54450.gf2 54450fr4 [1, -1, 1, -1103180, -2481056553] [2] 3317760

## Rank

sage: E.rank()

The elliptic curves in class 54450fr have rank $$0$$.

## Modular form 54450.2.a.gf

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.