Properties

Label 121275.cf
Number of curves 6
Conductor 121275
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("121275.cf1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 121275.cf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121275.cf1 121275eq6 [1, -1, 1, -49822205, -135345043578] [2] 7864320  
121275.cf2 121275eq4 [1, -1, 1, -3131330, -2089286328] [2, 2] 3932160  
121275.cf3 121275eq2 [1, -1, 1, -430205, 60809172] [2, 2] 1966080  
121275.cf4 121275eq1 [1, -1, 1, -375080, 88481922] [2] 983040 \(\Gamma_0(N)\)-optimal
121275.cf5 121275eq5 [1, -1, 1, 341545, -6472054578] [2] 7864320  
121275.cf6 121275eq3 [1, -1, 1, 1388920, 439187172] [2] 3932160  

Rank

sage: E.rank()
 

The elliptic curves in class 121275.cf have rank \(0\).

Modular form 121275.2.a.cf

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.