Properties

Label 76230.bk
Number of curves $4$
Conductor $76230$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("76230.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.bk1 76230i3 [1, -1, 0, -114549, 14932385] [2] 414720  
76230.bk2 76230i4 [1, -1, 0, -81879, 23603003] [2] 829440  
76230.bk3 76230i1 [1, -1, 0, -5649, -141795] [2] 138240 \(\Gamma_0(N)\)-optimal
76230.bk4 76230i2 [1, -1, 0, 8871, -760347] [2] 276480  

Rank

sage: E.rank()
 

The elliptic curves in class 76230.bk have rank \(1\).

Modular form 76230.2.a.bk

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.