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Properties

Label 76614.k
Number of curves $2$
Conductor $76614$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 76614.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
76614.k1 76614j2 \([1, 1, 1, -90928315, -3703679732491]\) \(-39934705050538129/2823126576537804\) \(-5877613323859927217144130636\) \([]\) \(45045504\) \(4.0081\)  
76614.k2 76614j1 \([1, 1, 1, -21209575, 37846168349]\) \(-506814405937489/4048994304\) \(-8429810787516658139136\) \([]\) \(6435072\) \(3.0352\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76614.k have rank \(0\).

Complex multiplication

The elliptic curves in class 76614.k do not have complex multiplication.

Modular form 76614.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.