# Properties

 Label 46546a Number of curves 4 Conductor 46546 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46546.a1")

sage: E.isogeny_class()

## Elliptic curves in class 46546a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46546.a4 46546a1 [1, 0, 1, -4136, 63030]  102816 $$\Gamma_0(N)$$-optimal
46546.a3 46546a2 [1, 0, 1, -58896, 5495222]  205632
46546.a2 46546a3 [1, 0, 1, -141036, -20395306]  308448
46546.a1 46546a4 [1, 0, 1, -154726, -16200690]  616896

## Rank

sage: E.rank()

The elliptic curves in class 46546a have rank $$0$$.

## Modular form 46546.2.a.a

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 