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Properties

Label 21175.bb
Number of curves $2$
Conductor $21175$
CM no
Rank $0$
Graph

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

Elliptic curves in class 21175.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
21175.bb1 21175bi2 \([1, 0, 1, -141331, -19343667]\) \(1409825840597/86806489\) \(19222873807416125\) \([2]\) \(161280\) \(1.8764\)  
21175.bb2 21175bi1 \([1, 0, 1, 6894, -1260217]\) \(163667323/3195731\) \(-707679050761375\) \([2]\) \(80640\) \(1.5298\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 21175.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 21175.bb do not have complex multiplication.

Modular form 21175.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{2} - 2 q^{3} - q^{4} - 2 q^{6} + q^{7} - 3 q^{8} + q^{9} + 2 q^{12} + 2 q^{13} + q^{14} - q^{16} + 2 q^{17} + q^{18} + O(q^{20})\) 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.