Properties

Label 287490.y
Number of curves $2$
Conductor $287490$
CM no
Rank $1$
Graph

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

Elliptic curves in class 287490.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
287490.y1 287490y2 \([1, 1, 0, -22896978167, 1333559082709269]\) \(517425559361898728438440369/38638656000\) \(99136220107466304000\) \([2]\) \(283668480\) \(4.2052\)  
287490.y2 287490y1 \([1, 1, 0, -1431058167, 20836504213269]\) \(-126323813482515646120369/1091629056000000\) \(-2800821497810939904000000\) \([2]\) \(141834240\) \(3.8586\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 287490.y have rank \(1\).

Complex multiplication

The elliptic curves in class 287490.y do not have complex multiplication.

Modular form 287490.2.a.y

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{11} - q^{12} - 2 q^{13} - q^{14} - q^{15} + q^{16} + 2 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.