# Properties

 Label 46475.b Number of curves 3 Conductor 46475 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46475.b1")

sage: E.isogeny_class()

## Elliptic curves in class 46475.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46475.b1 46475a3 [0, 1, 1, -33040908, -73112478656] [] 1512000
46475.b2 46475a2 [0, 1, 1, -43658, -6374156] [] 302400
46475.b3 46475a1 [0, 1, 1, -1408, 47844] [] 60480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 46475.b have rank $$1$$.

## Modular form 46475.2.a.b

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 