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Properties

Label 28050.c
Number of curves $4$
Conductor $28050$
CM no
Rank $1$
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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 28050.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.c1 28050f4 \([1, 1, 0, -2684275, 601601875]\) \(136894171818794254129/69177425857031250\) \(1080897279016113281250\) \([2]\) \(1966080\) \(2.7286\)  
28050.c2 28050f2 \([1, 1, 0, -2170025, 1228472625]\) \(72326626749631816849/69403061722500\) \(1084422839414062500\) \([2, 2]\) \(983040\) \(2.3820\)  
28050.c3 28050f1 \([1, 1, 0, -2169525, 1229068125]\) \(72276643492008825169/66646800\) \(1041356250000\) \([2]\) \(491520\) \(2.0354\) \(\Gamma_0(N)\)-optimal
28050.c4 28050f3 \([1, 1, 0, -1663775, 1817241375]\) \(-32597768919523300849/72509045805004050\) \(-1132953840703188281250\) \([2]\) \(1966080\) \(2.7286\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 28050.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.