# Properties

 Label 17661g Number of curves 2 Conductor 17661 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17661.c1")

sage: E.isogeny_class()

## Elliptic curves in class 17661g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17661.c2 17661g1 [1, 0, 0, -438, 76659]  26880 $$\Gamma_0(N)$$-optimal
17661.c1 17661g2 [1, 0, 0, -29873, 1966386]  53760

## Rank

sage: E.rank()

The elliptic curves in class 17661g have rank $$1$$.

## Modular form 17661.2.a.c

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 