Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("76230.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 76230t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
76230.c7 76230t1 [1, -1, 0, -541800, 153576000] [2] 1105920 \(\Gamma_0(N)\)-optimal
76230.c6 76230t2 [1, -1, 0, -628920, 100938096] [2, 2] 2211840  
76230.c5 76230t3 [1, -1, 0, -1603575, -593603235] [2] 3317760  
76230.c8 76230t4 [1, -1, 0, 2093580, 739636596] [2] 4423680  
76230.c4 76230t5 [1, -1, 0, -4745340, -3907631700] [2] 4423680  
76230.c2 76230t6 [1, -1, 0, -23906295, -44980476579] [2, 2] 6635520  
76230.c3 76230t7 [1, -1, 0, -22163895, -51816608739] [2] 13271040  
76230.c1 76230t8 [1, -1, 0, -382492215, -2879171871075] [2] 13271040  

Rank

sage: E.rank()
 

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

Modular form 76230.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} - 2q^{13} + q^{14} + q^{16} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.