Properties

Label 291018bi
Number of curves 2
Conductor 291018
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("291018.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 291018bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
291018.bi1 291018bi1 [1, 0, 1, -26331218, 52017132260] [] 22127616 \(\Gamma_0(N)\)-optimal
291018.bi2 291018bi2 [1, 0, 1, 146114692, -2296207961500] [] 154893312  

Rank

sage: E.rank()
 

The elliptic curves in class 291018bi have rank \(1\).

Modular form 291018.2.a.bi

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 2q^{11} + q^{12} + q^{14} + q^{15} + q^{16} + 4q^{17} - q^{18} + 8q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.