# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.c1")

sage: E.isogeny_class()

## Elliptic curves in class 46410.c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.c1 46410d4 [1, 1, 0, -240473, 45288633] [2] 294912
46410.c2 46410d2 [1, 1, 0, -15053, 700557] [2, 2] 147456
46410.c3 46410d3 [1, 1, 0, -5953, 1550497] [2] 294912
46410.c4 46410d1 [1, 1, 0, -1533, -5187] [2] 73728 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 46410.2.a.c

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.