Properties

Label 1290b
Number of curves $2$
Conductor $1290$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1290b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.b1 1290b1 \([1, 1, 0, -154527, -23386059]\) \(408076159454905367161/1190206406250000\) \(1190206406250000\) \([2]\) \(10560\) \(1.7632\) \(\Gamma_0(N)\)-optimal
1290.b2 1290b2 \([1, 1, 0, -92027, -42398559]\) \(-86193969101536367161/725294740213012500\) \(-725294740213012500\) \([2]\) \(21120\) \(2.1098\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1290b have rank \(0\).

Complex multiplication

The elliptic curves in class 1290b do not have complex multiplication.

Modular form 1290.2.a.b

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