Properties

Label 76230.de
Number of curves $6$
Conductor $76230$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("76230.de1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230.de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.de1 76230dk6 [1, -1, 1, -18295223, -30115405119] [2] 2621440  
76230.de2 76230dk4 [1, -1, 1, -1143473, -470320419] [2, 2] 1310720  
76230.de3 76230dk5 [1, -1, 1, -1067243, -535786743] [2] 2621440  
76230.de4 76230dk3 [1, -1, 1, -402953, 93154317] [2] 1310720  
76230.de5 76230dk2 [1, -1, 1, -76253, -6293163] [2, 2] 655360  
76230.de6 76230dk1 [1, -1, 1, 10867, -612939] [2] 327680 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 76230.2.a.de

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.