Properties

Label 379050.bi
Number of curves $2$
Conductor $379050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 379050.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
379050.bi1 379050bi2 \([1, 1, 0, -5645325, 11713195875]\) \(-43308090025/103996158\) \(-47779207751222636718750\) \([]\) \(43200000\) \(3.0399\)  
379050.bi2 379050bi1 \([1, 1, 0, -262815, -97319835]\) \(-1706927698345/2483133408\) \(-2920529970497311200\) \([]\) \(8640000\) \(2.2352\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 379050.bi have rank \(1\).

Complex multiplication

The elliptic curves in class 379050.bi do not have complex multiplication.

Modular form 379050.2.a.bi

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

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.