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Properties

Label 122694.bb
Number of curves $2$
Conductor $122694$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("bb1")
 
E.isogeny_class()
 

Elliptic curves in class 122694.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122694.bb1 122694bn2 \([1, 0, 1, -58821975, 170277638650]\) \(92162208697/2044416\) \(499296940861581113332224\) \([]\) \(36391680\) \(3.3349\)  
122694.bb2 122694bn1 \([1, 0, 1, -6983760, -7009056650]\) \(154241737/2376\) \(580277952964130942664\) \([]\) \(12130560\) \(2.7856\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 122694.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 122694.bb do not have complex multiplication.

Modular form 122694.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - 3 q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} + 3 q^{10} + q^{12} + 4 q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - q^{18} - 7 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.