Properties

Label 1734.j
Number of curves $6$
Conductor $1734$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1734.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1734.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1734.j1 1734i5 [1, 1, 1, -8018022, -8742084111] [2] 36864  
1734.j2 1734i3 [1, 1, 1, -501132, -136748439] [2, 2] 18432  
1734.j3 1734i6 [1, 1, 1, -475122, -151542927] [2] 36864  
1734.j4 1734i2 [1, 1, 1, -32952, -1912599] [2, 2] 9216  
1734.j5 1734i1 [1, 1, 1, -9832, 343913] [4] 4608 \(\Gamma_0(N)\)-optimal
1734.j6 1734i4 [1, 1, 1, 65308, -11031127] [2] 18432  

Rank

sage: E.rank()
 

The elliptic curves in class 1734.j have rank \(0\).

Modular form 1734.2.a.j

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} + q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 2q^{13} - 2q^{15} + q^{16} + q^{18} + 4q^{19} + O(q^{20}) \)

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.