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Properties

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

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 287490q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
287490.q2 287490q1 \([1, 1, 0, -317011292, -36369933689904]\) \(-69557303652860874433300957/11241080443431191524147200\) \(-569394447701120144272628121600\) \([2]\) \(491692032\) \(4.3889\) \(\Gamma_0(N)\)-optimal
287490.q1 287490q2 \([1, 1, 0, -18510828892, -961303594075184]\) \(13848289662603101746739261409757/132849458140481700073021440\) \(6729223603189819553798755000320\) \([2]\) \(983384064\) \(4.7355\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 287490.2.a.q

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.