Properties

Label 28050.f
Number of curves $2$
Conductor $28050$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 28050.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.f1 28050s2 \([1, 1, 0, -281325, 61912125]\) \(-1260727040508389/121448888352\) \(-237204860062500000\) \([]\) \(440000\) \(2.0753\)  
28050.f2 28050s1 \([1, 1, 0, 550, -272250]\) \(9393931/16427202\) \(-32084378906250\) \([]\) \(88000\) \(1.2706\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 28050.f have rank \(1\).

Complex multiplication

The elliptic curves in class 28050.f do not have complex multiplication.

Modular form 28050.2.a.f

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