# Properties

 Label 17850o Number of curves $6$ Conductor $17850$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("17850.t1")

sage: E.isogeny_class()

## Elliptic curves in class 17850o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17850.t5 17850o1 [1, 0, 1, -1756101, 894452848] [2] 491520 $$\Gamma_0(N)$$-optimal
17850.t4 17850o2 [1, 0, 1, -2268101, 330228848] [2, 2] 983040
17850.t2 17850o3 [1, 0, 1, -21476101, -38047355152] [2, 2] 1966080
17850.t6 17850o4 [1, 0, 1, 8747899, 2599524848] [2] 1966080
17850.t1 17850o5 [1, 0, 1, -342965101, -2444714009152] [2] 3932160
17850.t3 17850o6 [1, 0, 1, -7315101, -87469245152] [2] 3932160

## Rank

sage: E.rank()

The elliptic curves in class 17850o have rank $$0$$.

## Modular form 17850.2.a.t

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + 4q^{11} + q^{12} + 2q^{13} + q^{14} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 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.