Properties

Label 277350.bz
Number of curves $2$
Conductor $277350$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 277350.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
277350.bz1 277350bz2 [1, 1, 1, -7662996563, 258190358067281] [2] 447068160  
277350.bz2 277350bz1 [1, 1, 1, -474084563, 4119830163281] [2] 223534080 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 277350.bz have rank \(1\).

Complex multiplication

The elliptic curves in class 277350.bz do not have complex multiplication.

Modular form 277350.2.a.bz

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

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 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.