# Properties

 Label 17325.k Number of curves 6 Conductor 17325 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17325.k1")

sage: E.isogeny_class()

## Elliptic curves in class 17325.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17325.k1 17325u5 [1, -1, 1, -1016780, 394882472] [2] 163840
17325.k2 17325u3 [1, -1, 1, -63905, 6109472] [2, 2] 81920
17325.k3 17325u2 [1, -1, 1, -8780, -174778] [2, 2] 40960
17325.k4 17325u1 [1, -1, 1, -7655, -255778] [2] 20480 $$\Gamma_0(N)$$-optimal
17325.k5 17325u6 [1, -1, 1, 6970, 18866972] [2] 163840
17325.k6 17325u4 [1, -1, 1, 28345, -1288528] [2] 81920

## Rank

sage: E.rank()

The elliptic curves in class 17325.k have rank $$1$$.

## Modular form 17325.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - q^{7} + 3q^{8} + q^{11} - 6q^{13} + q^{14} - q^{16} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.