# Properties

 Label 47610bz Number of curves 8 Conductor 47610 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("47610.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 47610bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47610.bu8 47610bz1 [1, -1, 1, 7042, 696701] [2] 202752 $$\Gamma_0(N)$$-optimal
47610.bu6 47610bz2 [1, -1, 1, -88178, 9152237] [2, 2] 405504
47610.bu7 47610bz3 [1, -1, 1, -64373, -20556403] [2] 608256
47610.bu5 47610bz4 [1, -1, 1, -326228, -61691443] [2] 811008
47610.bu4 47610bz5 [1, -1, 1, -1373648, 620007581] [2] 811008
47610.bu3 47610bz6 [1, -1, 1, -1587893, -768300019] [2, 2] 1216512
47610.bu1 47610bz7 [1, -1, 1, -25392893, -49244802019] [2] 2433024
47610.bu2 47610bz8 [1, -1, 1, -2159213, -165671683] [2] 2433024

## Rank

sage: E.rank()

The elliptic curves in class 47610bz have rank $$0$$.

## Modular form 47610.2.a.bu

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 4q^{7} + q^{8} - q^{10} + 2q^{13} + 4q^{14} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.