Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 121275.bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
121275.bt1 121275en6 [1, -1, 1, -33617430230, -2372429651687728] [2] 70778880  
121275.bt2 121275en4 [1, -1, 1, -2101089605, -37068811375228] [2, 2] 35389440  
121275.bt3 121275en5 [1, -1, 1, -2090670980, -37454633896228] [2] 70778880  
121275.bt4 121275en3 [1, -1, 1, -280531355, 953779972772] [2] 35389440  
121275.bt5 121275en2 [1, -1, 1, -131969480, -573138978478] [2, 2] 17694720  
121275.bt6 121275en1 [1, -1, 1, 385645, -26777022478] [2] 8847360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 121275.bt do not have complex multiplication.

Modular form 121275.2.a.bt

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.