Properties

Label 350d
Number of curves 6
Conductor 350
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("350.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 350d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
350.f5 350d1 [1, 1, 1, -13, 31] [2] 48 \(\Gamma_0(N)\)-optimal
350.f4 350d2 [1, 1, 1, -263, 1531] [2] 96  
350.f6 350d3 [1, 1, 1, 112, -719] [2] 144  
350.f3 350d4 [1, 1, 1, -888, -8719] [2] 288  
350.f2 350d5 [1, 1, 1, -4263, -109219] [2] 432  
350.f1 350d6 [1, 1, 1, -68263, -6893219] [2] 864  

Rank

sage: E.rank()
 

The elliptic curves in class 350d have rank \(0\).

Modular form 350.2.a.f

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} + q^{4} + 2q^{6} - q^{7} + q^{8} + q^{9} + 2q^{12} + 4q^{13} - q^{14} + q^{16} - 6q^{17} + q^{18} + 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.