# Properties

 Label 46410.b Number of curves 4 Conductor 46410 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.b1")

sage: E.isogeny_class()

## Elliptic curves in class 46410.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.b1 46410c4 [1, 1, 0, -516418, 138505948]  688128
46410.b2 46410c2 [1, 1, 0, -79018, -5573612] [2, 2] 344064
46410.b3 46410c1 [1, 1, 0, -71018, -7312812]  172032 $$\Gamma_0(N)$$-optimal
46410.b4 46410c3 [1, 1, 0, 230382, -38184372]  688128

## Rank

sage: E.rank()

The elliptic curves in class 46410.b have rank $$0$$.

## Modular form 46410.2.a.b

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 