Properties

Label 67158.q
Number of curves 2
Conductor 67158
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("67158.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 67158.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67158.q1 67158r1 [1, -1, 0, -1402254, -638940204] [] 1053696 \(\Gamma_0(N)\)-optimal
67158.q2 67158r2 [1, -1, 0, 7781256, 28217419146] [] 7375872  

Rank

sage: E.rank()
 

The elliptic curves in class 67158.q have rank \(0\).

Modular form 67158.2.a.q

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

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.