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Properties

Label 38962.bf
Number of curves $2$
Conductor $38962$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 38962.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.bf1 38962w2 \([1, 1, 1, -73268, -7176971]\) \(24553362849625/1755162752\) \(3109377880095872\) \([2]\) \(286720\) \(1.7197\)  
38962.bf2 38962w1 \([1, 1, 1, 4172, -486155]\) \(4533086375/60669952\) \(-107480520835072\) \([2]\) \(143360\) \(1.3731\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38962.bf have rank \(1\).

Complex multiplication

The elliptic curves in class 38962.bf do not have complex multiplication.

Modular form 38962.2.a.bf

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.