# Properties

 Label 17787u Number of curves 4 Conductor 17787 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17787.o1")

sage: E.isogeny_class()

## Elliptic curves in class 17787u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17787.o3 17787u1 [1, 0, 0, -38662, -2904637]  51840 $$\Gamma_0(N)$$-optimal
17787.o2 17787u2 [1, 0, 0, -68307, 2152800] [2, 2] 103680
17787.o1 17787u3 [1, 0, 0, -868722, 311273073]  207360
17787.o4 17787u4 [1, 0, 0, 257788, 16827075]  207360

## Rank

sage: E.rank()

The elliptic curves in class 17787u have rank $$0$$.

## Modular form 17787.2.a.o

sage: E.q_eigenform(10)

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

## 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. 