# Properties

 Label 61446.cv Number of curves 2 Conductor 61446 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61446.cv1")
sage: E.isogeny_class()

## Elliptic curves in class 61446.cv

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
61446.cv1 61446de2 [1, 0, 0, -16743266, -11929605948] 7 6750240
61446.cv2 61446de1 [1, 0, 0, -14044626, -20259954786] 1 964320 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 61446.cv have rank $$0$$.

## Modular form 61446.2.a.cv

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + q^{11} + q^{12} - q^{15} + q^{16} - 3q^{17} + q^{18} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 