# Properties

 Label 4400t Number of curves 4 Conductor 4400 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4400.e1")

sage: E.isogeny_class()

## Elliptic curves in class 4400t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4400.e4 4400t1 [0, 1, 0, -1133, -14762]  3456 $$\Gamma_0(N)$$-optimal
4400.e3 4400t2 [0, 1, 0, -2508, 26488]  6912
4400.e2 4400t3 [0, 1, 0, -11133, 442738]  10368
4400.e1 4400t4 [0, 1, 0, -177508, 28726488]  20736

## Rank

sage: E.rank()

The elliptic curves in class 4400t have rank $$1$$.

## Modular form4400.2.a.e

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 