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Properties

Label 38.b
Number of curves $2$
Conductor $38$
CM no
Rank $0$
Graph

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

Elliptic curves in class 38.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38.b1 38b2 [1, 1, 1, -70, -279] [] 10  
38.b2 38b1 [1, 1, 1, 0, 1] [5] 2 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38.b have rank \(0\).

Complex multiplication

The elliptic curves in class 38.b do not have complex multiplication.

Modular form 38.2.a.b

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - 4q^{5} - q^{6} + 3q^{7} + q^{8} - 2q^{9} - 4q^{10} + 2q^{11} - q^{12} - q^{13} + 3q^{14} + 4q^{15} + q^{16} + 3q^{17} - 2q^{18} - q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.