# Properties

 Label 54150t Number of curves $2$ Conductor $54150$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("54150.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 54150t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54150.bk2 54150t1 [1, 0, 1, -21330776, 1919420198] [2] 14008320 $$\Gamma_0(N)$$-optimal
54150.bk1 54150t2 [1, 0, 1, -240818776, 1434737084198] [2] 28016640

## Rank

sage: E.rank()

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

## Modular form 54150.2.a.bk

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.