# Properties

 Label 46410m Number of curves 2 Conductor 46410 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.m1")

sage: E.isogeny_class()

## Elliptic curves in class 46410m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.m2 46410m1 [1, 1, 0, -9327, 402021] [2] 138240 $$\Gamma_0(N)$$-optimal
46410.m1 46410m2 [1, 1, 0, -156207, 23697189] [2] 276480

## Rank

sage: E.rank()

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

## Modular form 46410.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} - q^{12} + q^{13} + q^{14} - q^{15} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.