# Properties

 Label 46410be Number of curves 8 Conductor 46410 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.be1")
sage: E.isogeny_class()

## Elliptic curves in class 46410be

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
46410.be7 46410be1 [1, 0, 1, -63473, -4407244] 6 304128 $$\Gamma_0(N)$$-optimal
46410.be6 46410be2 [1, 0, 1, -375973, 85217756] 12 608256
46410.be4 46410be3 [1, 0, 1, -4722848, -3950910994] 2 912384
46410.be8 46410be4 [1, 0, 1, 197777, 322291256] 6 1216512
46410.be2 46410be5 [1, 0, 1, -5949723, 5585394256] 6 1216512
46410.be3 46410be6 [1, 0, 1, -4730848, -3936856594] 4 1824768
46410.be5 46410be7 [1, 0, 1, -1783048, -8785398034] 2 3649536
46410.be1 46410be8 [1, 0, 1, -7806648, 1811198446] 2 3649536

## Rank

sage: E.rank()

The elliptic curves in class 46410be have rank $$1$$.

## Modular form None

sage: E.q_eigenform(10)
$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + q^{12} + q^{13} - q^{14} + q^{15} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.