Properties

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

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 277350.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
277350.ba1 277350ba2 \([1, 1, 0, -319915, 51433525]\) \(4582567781/1198152\) \(946744222485681000\) \([2]\) \(5677056\) \(2.1582\)  
277350.ba2 277350ba1 \([1, 1, 0, 49885, 5208525]\) \(17373979/24768\) \(-19570939999704000\) \([2]\) \(2838528\) \(1.8116\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 277350.2.a.ba

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