Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("76230.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.cv2 76230ct1 [1, -1, 1, -12728, -548809] [2] 138240 \(\Gamma_0(N)\)-optimal
76230.cv3 76230ct2 [1, -1, 1, -9098, -871153] [2] 276480  
76230.cv1 76230ct3 [1, -1, 1, -50843, 3879307] [2] 414720  
76230.cv4 76230ct4 [1, -1, 1, 79837, 20449531] [2] 829440  

Rank

sage: E.rank()
 

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

Modular form 76230.2.a.cv

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 Cremona 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 Cremona labels.