Properties

Label 190575ed
Number of curves $6$
Conductor $190575$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("ed1")
 
E.isogeny_class()
 

Elliptic curves in class 190575ed

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.dh4 190575ed1 \([1, -1, 0, -7215192, 7461440091]\) \(2058561081361/12705\) \(256376571033515625\) \([2]\) \(5898240\) \(2.5271\) \(\Gamma_0(N)\)-optimal
190575.dh3 190575ed2 \([1, -1, 0, -7351317, 7165368216]\) \(2177286259681/161417025\) \(3257264334980816015625\) \([2, 2]\) \(11796480\) \(2.8737\)  
190575.dh5 190575ed3 \([1, -1, 0, 6941808, 31649491341]\) \(1833318007919/22507682505\) \(-454186734556705974140625\) \([2]\) \(23592960\) \(3.2203\)  
190575.dh2 190575ed4 \([1, -1, 0, -23822442, -36268988409]\) \(74093292126001/14707625625\) \(296787928042673525390625\) \([2, 2]\) \(23592960\) \(3.2203\)  
190575.dh6 190575ed5 \([1, -1, 0, 49548933, -215662000284]\) \(666688497209279/1381398046875\) \(-27875489530909735107421875\) \([2]\) \(47185920\) \(3.5668\)  
190575.dh1 190575ed6 \([1, -1, 0, -360731817, -2636872454034]\) \(257260669489908001/14267882475\) \(287914268779983488671875\) \([2]\) \(47185920\) \(3.5668\)  

Rank

sage: E.rank()
 

The elliptic curves in class 190575ed have rank \(1\).

Complex multiplication

The elliptic curves in class 190575ed do not have complex multiplication.

Modular form 190575.2.a.ed

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