# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.d1")

sage: E.isogeny_class()

## Elliptic curves in class 46410a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.d4 46410a1 [1, 1, 0, -1735564903, -15959344729547] [2] 63406080 $$\Gamma_0(N)$$-optimal
46410.d2 46410a2 [1, 1, 0, -24333584823, -1460601042571323] [2, 2] 126812160
46410.d3 46410a3 [1, 1, 0, -20930167323, -1883681914046823] [2] 253624320
46410.d1 46410a4 [1, 1, 0, -389305321043, -93494136872571087] [2] 253624320

## Rank

sage: E.rank()

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

## Modular form 46410.2.a.d

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 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.