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Properties

Label 38962.z
Number of curves $2$
Conductor $38962$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 38962.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38962.z1 38962bd2 \([1, -1, 1, -28821, -1870129]\) \(1494447319737/5411854\) \(9587429484094\) \([2]\) \(122880\) \(1.3520\)  
38962.z2 38962bd1 \([1, -1, 1, -991, -55613]\) \(-60698457/725788\) \(-1285777715068\) \([2]\) \(61440\) \(1.0054\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38962.z have rank \(0\).

Complex multiplication

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

Modular form 38962.2.a.z

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