# Properties

 Label 46410.a Number of curves 4 Conductor 46410 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.a1")

sage: E.isogeny_class()

## Elliptic curves in class 46410.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.a1 46410b4 [1, 1, 0, -41093, -2836347]  294912
46410.a2 46410b2 [1, 1, 0, -10493, 364413] [2, 2] 147456
46410.a3 46410b1 [1, 1, 0, -10173, 390717]  73728 $$\Gamma_0(N)$$-optimal
46410.a4 46410b3 [1, 1, 0, 14987, 1888117]  294912

## Rank

sage: E.rank()

The elliptic curves in class 46410.a have rank $$2$$.

## Modular form 46410.2.a.a

sage: E.q_eigenform(10)

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

## 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. 