# Properties

 Label 41280.ct Number of curves $4$ Conductor $41280$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ct1")

sage: E.isogeny_class()

## Elliptic curves in class 41280.ct

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
41280.ct1 41280dk4 [0, 1, 0, -53665, -4770337] [2] 147456
41280.ct2 41280dk2 [0, 1, 0, -5665, 39263] [2, 2] 73728
41280.ct3 41280dk1 [0, 1, 0, -4385, 110175] [2] 36864 $$\Gamma_0(N)$$-optimal
41280.ct4 41280dk3 [0, 1, 0, 21855, 330975] [4] 147456

## Rank

sage: E.rank()

The elliptic curves in class 41280.ct have rank $$0$$.

## Complex multiplication

The elliptic curves in class 41280.ct do not have complex multiplication.

## Modular form 41280.2.a.ct

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 4q^{7} + q^{9} + 2q^{13} + q^{15} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels.