Properties

Label 28050x
Number of curves $6$
Conductor $28050$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 28050x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
28050.bh5 28050x1 \([1, 0, 1, -7101, 173848]\) \(2533811507137/625016832\) \(9765888000000\) \([2]\) \(65536\) \(1.2029\) \(\Gamma_0(N)\)-optimal
28050.bh4 28050x2 \([1, 0, 1, -39101, -2834152]\) \(423108074414017/23284318464\) \(363817476000000\) \([2, 2]\) \(131072\) \(1.5495\)  
28050.bh6 28050x3 \([1, 0, 1, 26899, -11414152]\) \(137763859017023/3683199928848\) \(-57549998888250000\) \([2]\) \(262144\) \(1.8961\)  
28050.bh2 28050x4 \([1, 0, 1, -617101, -186638152]\) \(1663303207415737537/5483698704\) \(85682792250000\) \([2, 2]\) \(262144\) \(1.8961\)  
28050.bh3 28050x5 \([1, 0, 1, -608601, -192027152]\) \(-1595514095015181697/95635786040388\) \(-1494309156881062500\) \([2]\) \(524288\) \(2.2426\)  
28050.bh1 28050x6 \([1, 0, 1, -9873601, -11942393152]\) \(6812873765474836663297/74052\) \(1157062500\) \([2]\) \(524288\) \(2.2426\)  

Rank

sage: E.rank()
 

The elliptic curves in class 28050x have rank \(0\).

Complex multiplication

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

Modular form 28050.2.a.x

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.