Properties

Label 76230du
Number of curves 8
Conductor 76230
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("76230.dr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230du

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.dr7 76230du1 [1, -1, 1, 228667, 31657277] [2] 1310720 \(\Gamma_0(N)\)-optimal
76230.dr6 76230du2 [1, -1, 1, -1165253, 284235581] [2, 2] 2621440  
76230.dr5 76230du3 [1, -1, 1, -8221973, -8869741603] [2, 2] 5242880  
76230.dr4 76230du4 [1, -1, 1, -16411253, 25586497181] [2] 5242880  
76230.dr8 76230du5 [1, -1, 1, 1383007, -28360167019] [2] 10485760  
76230.dr2 76230du6 [1, -1, 1, -130734473, -575318536603] [2, 2] 10485760  
76230.dr3 76230du7 [1, -1, 1, -129917723, -582862366303] [2] 20971520  
76230.dr1 76230du8 [1, -1, 1, -2091751223, -36821967736903] [2] 20971520  

Rank

sage: E.rank()
 

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

Modular form 76230.2.a.dr

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.