Properties

Label 49.a
Number of curves $4$
Conductor $49$
CM -7
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("49.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 49.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
49.a1 49a4 [1, -1, 0, -1822, 30393] [2] 14  
49.a2 49a3 [1, -1, 0, -107, 552] [2] 7  
49.a3 49a2 [1, -1, 0, -37, -78] [2] 2  
49.a4 49a1 [1, -1, 0, -2, -1] [2] 1 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 49.a have rank \(0\).

Modular form 49.2.a.a

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.