Properties

Label 79350.k
Number of curves $6$
Conductor $79350$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("79350.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 79350.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
79350.k1 79350e4 [1, 1, 0, -1460040275, -21473739057375] [2] 19464192  
79350.k2 79350e6 [1, 1, 0, -341602025, 2081475474375] [2] 38928384  
79350.k3 79350e3 [1, 1, 0, -93633275, -317126244375] [2, 2] 19464192  
79350.k4 79350e2 [1, 1, 0, -91252775, -335553694875] [2, 2] 9732096  
79350.k5 79350e1 [1, 1, 0, -5554775, -5530696875] [2] 4866048 \(\Gamma_0(N)\)-optimal
79350.k6 79350e5 [1, 1, 0, 116247475, -1536323521125] [2] 38928384  

Rank

sage: E.rank()
 

The elliptic curves in class 79350.k have rank \(0\).

Modular form 79350.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4q^{11} - q^{12} + 2q^{13} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.