Properties

Label 350a
Number of curves $4$
Conductor $350$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("350.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 350a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
350.b4 350a1 [1, -1, 0, 58, -284] [2] 96 \(\Gamma_0(N)\)-optimal
350.b3 350a2 [1, -1, 0, -442, -2784] [2, 2] 192  
350.b1 350a3 [1, -1, 0, -6692, -209034] [2] 384  
350.b2 350a4 [1, -1, 0, -2192, 37466] [2] 384  

Rank

sage: E.rank()
 

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

Modular form 350.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{7} - q^{8} - 3q^{9} + 4q^{11} + 6q^{13} - q^{14} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.