# Properties

 Label 61017a Number of curves 4 Conductor 61017 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61017.a1")

sage: E.isogeny_class()

## Elliptic curves in class 61017a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61017.a3 61017a1 [1, 0, 0, -12057, 504288]  121968 $$\Gamma_0(N)$$-optimal
61017.a2 61017a2 [1, 0, 0, -21302, -377685] [2, 2] 243936
61017.a4 61017a3 [1, 0, 0, 80393, -2920060]  487872
61017.a1 61017a4 [1, 0, 0, -270917, -54244602]  487872

## Rank

sage: E.rank()

The elliptic curves in class 61017a have rank $$0$$.

## Modular form 61017.2.a.a

sage: E.q_eigenform(10)

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

## 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. 