# Properties

 Label 476850.br Number of curves 6 Conductor 476850 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("476850.br1")

sage: E.isogeny_class()

## Elliptic curves in class 476850.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
476850.br1 476850br6 [1, 1, 0, -2110711650, -37320720081750] [u'2'] 339738624
476850.br2 476850br4 [1, 1, 0, -143705400, -472792000500] [u'2', u'2'] 169869312
476850.br3 476850br2 [1, 1, 0, -53392900, 144313312000] [u'2', u'2'] 84934656
476850.br4 476850br1 [1, 1, 0, -52814900, 147712530000] [u'2'] 42467328 $$\Gamma_0(N)$$-optimal
476850.br5 476850br3 [1, 1, 0, 27671600, 543880232500] [u'2'] 169869312
476850.br6 476850br5 [1, 1, 0, 378300850, -3117797669250] [u'2'] 339738624

## Rank

sage: E.rank()

The elliptic curves in class 476850.br have rank $$0$$.

## Modular form 476850.2.a.br

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + q^{11} - q^{12} - 6q^{13} + q^{16} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.