# Properties

 Label 54150ct Number of curves $4$ Conductor $54150$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54150.ci1")

sage: E.isogeny_class()

## Elliptic curves in class 54150ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.ci4 54150ct1 [1, 0, 0, -90438, -17870508] [4] 829440 $$\Gamma_0(N)$$-optimal
54150.ci3 54150ct2 [1, 0, 0, -1714938, -864235008] [2, 2] 1658880
54150.ci2 54150ct3 [1, 0, 0, -1985688, -573178758] [2] 3317760
54150.ci1 54150ct4 [1, 0, 0, -27436188, -55316121258] [2] 3317760

## Rank

sage: E.rank()

The elliptic curves in class 54150ct have rank $$0$$.

## Modular form 54150.2.a.ci

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - 4q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} - 2q^{13} - 4q^{14} + q^{16} + 2q^{17} + q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.