# Properties

 Label 5746e Number of curves 4 Conductor 5746 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5746.b1")

sage: E.isogeny_class()

## Elliptic curves in class 5746e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5746.b4 5746e1 [1, 0, 1, -511, 2706] [2] 4608 $$\Gamma_0(N)$$-optimal
5746.b3 5746e2 [1, 0, 1, -7271, 237954] [2] 9216
5746.b2 5746e3 [1, 0, 1, -17411, -885558] [2] 13824
5746.b1 5746e4 [1, 0, 1, -19101, -703714] [2] 27648

## Rank

sage: E.rank()

The elliptic curves in class 5746e have rank $$1$$.

## Modular form5746.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + 2q^{6} + 4q^{7} - q^{8} + q^{9} - 6q^{11} - 2q^{12} - 4q^{14} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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.