# Properties

 Label 17238.e Number of curves 6 Conductor 17238 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17238.e1")

sage: E.isogeny_class()

## Elliptic curves in class 17238.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17238.e1 17238f5 [1, 0, 1, -4688740, -3908190232] [2] 294912
17238.e2 17238f3 [1, 0, 1, -293050, -61082344] [2, 2] 147456
17238.e3 17238f6 [1, 0, 1, -277840, -67701736] [2] 294912
17238.e4 17238f2 [1, 0, 1, -19270, -850744] [2, 2] 73728
17238.e5 17238f1 [1, 0, 1, -5750, 155144] [2] 36864 $$\Gamma_0(N)$$-optimal
17238.e6 17238f4 [1, 0, 1, 38190, -4941896] [2] 147456

## Rank

sage: E.rank()

The elliptic curves in class 17238.e have rank $$1$$.

## Modular form 17238.2.a.e

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.