# Properties

 Label 44880cy Number of curves 6 Conductor 44880 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("44880.cu1")

sage: E.isogeny_class()

## Elliptic curves in class 44880cy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44880.cu4 44880cy1 [0, 1, 0, -116960, -15434892] [2] 147456 $$\Gamma_0(N)$$-optimal
44880.cu3 44880cy2 [0, 1, 0, -118240, -15081100] [2, 2] 294912
44880.cu5 44880cy3 [0, 1, 0, 61280, -56657932] [2] 589824
44880.cu2 44880cy4 [0, 1, 0, -318240, 49158900] [2, 4] 589824
44880.cu6 44880cy5 [0, 1, 0, 837760, 325211700] [4] 1179648
44880.cu1 44880cy6 [0, 1, 0, -4674240, 3887666100] [4] 1179648

## Rank

sage: E.rank()

The elliptic curves in class 44880cy have rank $$0$$.

## Modular form 44880.2.a.cu

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} + q^{11} + 6q^{13} + q^{15} + q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.