# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17325.p1")

sage: E.isogeny_class()

## Elliptic curves in class 17325.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17325.p1 17325y5 [1, -1, 1, -2981255, 1981934372] [2] 393216
17325.p2 17325y3 [1, -1, 1, -196880, 27303122] [2, 2] 196608
17325.p3 17325y2 [1, -1, 1, -60755, -5366878] [2, 2] 98304
17325.p4 17325y1 [1, -1, 1, -59630, -5589628] [2] 49152 $$\Gamma_0(N)$$-optimal
17325.p5 17325y4 [1, -1, 1, 57370, -23794378] [2] 196608
17325.p6 17325y6 [1, -1, 1, 409495, 161918372] [2] 393216

## Rank

sage: E.rank()

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

## Modular form 17325.2.a.p

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.