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Properties

Label 25350bf
Number of curves $2$
Conductor $25350$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 25350bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
25350.y2 25350bf1 \([1, 0, 1, -60046211, -196208032642]\) \(-198417696411528597145/22989483914821632\) \(-2774146196635407168307200\) \([]\) \(5644800\) \(3.4265\) \(\Gamma_0(N)\)-optimal
25350.y1 25350bf2 \([1, 0, 1, -38516158451, -2909464347279202]\) \(-134057911417971280740025/1872\) \(-88240102031250000\) \([]\) \(28224000\) \(4.2312\)  

Rank

sage: E.rank()
 

The elliptic curves in class 25350bf have rank \(0\).

Complex multiplication

The elliptic curves in class 25350bf do not have complex multiplication.

Modular form 25350.2.a.bf

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