Properties

Label 1288i
Number of curves $2$
Conductor $1288$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1288i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1288.g2 1288i1 \([0, -1, 0, -2632, 52860]\) \(1969910093092/7889\) \(8078336\) \([2]\) \(480\) \(0.53679\) \(\Gamma_0(N)\)-optimal
1288.g1 1288i2 \([0, -1, 0, -2672, 51212]\) \(1030541881826/62236321\) \(127459985408\) \([2]\) \(960\) \(0.88336\)  

Rank

sage: E.rank()
 

The elliptic curves in class 1288i have rank \(0\).

Complex multiplication

The elliptic curves in class 1288i do not have complex multiplication.

Modular form 1288.2.a.i

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} + 2 q^{5} + q^{7} + q^{9} + 2 q^{11} + 4 q^{13} + 4 q^{15} - 2 q^{17} + O(q^{20})\) 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.