Properties

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

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

Elliptic curves in class 17850.t

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

Rank

sage: E.rank()
 

The elliptic curves in class 17850.t 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 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.