# Properties

 Label 4410.b Number of curves 4 Conductor 4410 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("4410.b1")

sage: E.isogeny_class()

## Elliptic curves in class 4410.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.b1 4410m3 [1, -1, 0, -118050, -15581350]  24576
4410.b2 4410m4 [1, -1, 0, -38670, 2744846]  24576
4410.b3 4410m2 [1, -1, 0, -7800, -212500] [2, 2] 12288
4410.b4 4410m1 [1, -1, 0, 1020, -20224]  6144 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4410.b have rank $$1$$.

## Modular form4410.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} + 6q^{13} + q^{16} + 2q^{17} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 