Properties

Label 238050.fn
Number of curves $6$
Conductor $238050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("238050.fn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 238050.fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
238050.fn1 238050fn3 [1, -1, 1, -13140362480, 579777814186647] [2] 155713536  
238050.fn2 238050fn6 [1, -1, 1, -3074418230, -56202912226353] [2] 311427072  
238050.fn3 238050fn4 [1, -1, 1, -842699480, 8561565898647] [2, 2] 155713536  
238050.fn4 238050fn2 [1, -1, 1, -821274980, 9059128486647] [2, 2] 77856768  
238050.fn5 238050fn1 [1, -1, 1, -49992980, 149278822647] [2] 38928384 \(\Gamma_0(N)\)-optimal
238050.fn6 238050fn5 [1, -1, 1, 1046227270, 41481781297647] [2] 311427072  

Rank

sage: E.rank()
 

The elliptic curves in class 238050.fn have rank \(0\).

Modular form 238050.2.a.fn

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.