# Properties

 Label 46410s Number of curves 4 Conductor 46410 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.n1")

sage: E.isogeny_class()

## Elliptic curves in class 46410s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.n4 46410s1 [1, 1, 0, -5427, -3219] [2] 110592 $$\Gamma_0(N)$$-optimal
46410.n2 46410s2 [1, 1, 0, -59507, 5545389] [2, 2] 221184
46410.n3 46410s3 [1, 1, 0, -32987, 10547061] [2] 442368
46410.n1 46410s4 [1, 1, 0, -951307, 356736229] [2] 442368

## Rank

sage: E.rank()

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

## Modular form 46410.2.a.n

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.