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Properties

Label 121275.bu
Number of curves $2$
Conductor $121275$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 121275.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
121275.bu1 121275bg2 \([1, -1, 1, -183980, 30252772]\) \(19034163/121\) \(4378092457921875\) \([2]\) \(691200\) \(1.8383\)  
121275.bu2 121275bg1 \([1, -1, 1, -18605, -176228]\) \(19683/11\) \(398008405265625\) \([2]\) \(345600\) \(1.4917\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 121275.bu have rank \(1\).

Complex multiplication

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

Modular form 121275.2.a.bu

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

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.