Properties

Label 76230.fg
Number of curves $4$
Conductor $76230$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("76230.fg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230.fg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.fg1 76230fe4 [1, -1, 1, -291512, -60504551] [2] 655360  
76230.fg2 76230fe3 [1, -1, 1, -95492, 10637641] [2] 655360  
76230.fg3 76230fe2 [1, -1, 1, -19262, -827351] [2, 2] 327680  
76230.fg4 76230fe1 [1, -1, 1, 2518, -78119] [2] 163840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 76230.fg have rank \(0\).

Modular form 76230.2.a.fg

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{5} + q^{7} + q^{8} + q^{10} + 6q^{13} + q^{14} + q^{16} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.