# Properties

 Label 4400m Number of curves 3 Conductor 4400 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4400.i1")

sage: E.isogeny_class()

## Elliptic curves in class 4400m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4400.i3 4400m1 [0, -1, 0, -133, -1363] [] 1120 $$\Gamma_0(N)$$-optimal
4400.i2 4400m2 [0, -1, 0, -4133, 186637] [] 5600
4400.i1 4400m3 [0, -1, 0, -3128133, 2130534637] [] 28000

## Rank

sage: E.rank()

The elliptic curves in class 4400m have rank $$0$$.

## Modular form4400.2.a.i

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{7} - 2q^{9} - q^{11} - 4q^{13} + 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.