Properties

Label 235950.y
Number of curves $2$
Conductor $235950$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 235950.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
235950.y1 235950y2 \([1, 1, 0, -1485200, -444096000]\) \(139370512222423/47971512576\) \(124707193825500000000\) \([2]\) \(7864320\) \(2.5579\)  
235950.y2 235950y1 \([1, 1, 0, 274800, -48096000]\) \(882802050857/897122304\) \(-2332167552000000000\) \([2]\) \(3932160\) \(2.2113\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 235950.y have rank \(2\).

Complex multiplication

The elliptic curves in class 235950.y do not have complex multiplication.

Modular form 235950.2.a.y

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.