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Properties

Label 19950.bb
Number of curves $2$
Conductor $19950$
CM no
Rank $1$
Graph

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

Elliptic curves in class 19950.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19950.bb1 19950bb2 \([1, 0, 1, -9144951, 10643612548]\) \(43304971114320697781/296432262\) \(578969261718750\) \([2]\) \(552960\) \(2.4326\)  
19950.bb2 19950bb1 \([1, 0, 1, -571201, 166490048]\) \(-10552599539268821/27662978028\) \(-54029253960937500\) \([2]\) \(276480\) \(2.0861\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19950.bb have rank \(1\).

Complex multiplication

The elliptic curves in class 19950.bb do not have complex multiplication.

Modular form 19950.2.a.bb

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + 4 q^{11} + q^{12} + 4 q^{13} + q^{14} + q^{16} - 2 q^{17} - q^{18} - q^{19} + O(q^{20})\) 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.