Properties

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

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 1290.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1290.i1 1290i2 \([1, 0, 1, -28, -52]\) \(2305199161/277350\) \(277350\) \([2]\) \(224\) \(-0.22485\)  
1290.i2 1290i1 \([1, 0, 1, 2, -4]\) \(1685159/7740\) \(-7740\) \([2]\) \(112\) \(-0.57142\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1290.2.a.i

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