# Properties

 Label 4410t Number of curves 6 Conductor 4410 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.l1")

sage: E.isogeny_class()

## Elliptic curves in class 4410t

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.l6 4410t1 [1, -1, 0, 4401, -158355] [2] 12288 $$\Gamma_0(N)$$-optimal
4410.l5 4410t2 [1, -1, 0, -30879, -1618947] [2, 2] 24576
4410.l2 4410t3 [1, -1, 0, -463059, -121159935] [2, 2] 49152
4410.l4 4410t4 [1, -1, 0, -163179, 24020793] [2] 49152
4410.l1 4410t5 [1, -1, 0, -7408809, -7760095785] [2] 98304
4410.l3 4410t6 [1, -1, 0, -432189, -138033477] [2] 98304

## Rank

sage: E.rank()

The elliptic curves in class 4410t have rank $$0$$.

## Modular form4410.2.a.l

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4q^{11} + 2q^{13} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.