# Properties

 Label 17787h Number of curves 6 Conductor 17787 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17787.s1")
sage: E.isogeny_class()

## Elliptic curves in class 17787h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
17787.s6 17787h1 [1, 1, 0, 5806, -35097] 2 30720 $$\Gamma_0(N)$$-optimal
17787.s5 17787h2 [1, 1, 0, -23839, -313760] 4 61440
17787.s2 17787h3 [1, 1, 0, -290644, -60344885] 4 122880
17787.s3 17787h4 [1, 1, 0, -231354, 42475833] 2 122880
17787.s1 17787h5 [1, 1, 0, -4648459, -3859488002] 2 245760
17787.s4 17787h6 [1, 1, 0, -201709, -97857668] 2 245760

## Rank

sage: E.rank()

The elliptic curves in class 17787h have rank $$1$$.

## Modular form 17787.2.a.s

sage: E.q_eigenform(10)
$$q + q^{2} - q^{3} - q^{4} + 2q^{5} - q^{6} - 3q^{8} + q^{9} + 2q^{10} + q^{12} - 2q^{13} - 2q^{15} - q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.