Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 1288d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1288.h2 1288d1 \([0, -1, 0, 84, -172]\) \(253012016/181447\) \(-46450432\) \([2]\) \(480\) \(0.15956\) \(\Gamma_0(N)\)-optimal
1288.h1 1288d2 \([0, -1, 0, -376, -1092]\) \(5756278756/2705927\) \(2770869248\) \([2]\) \(960\) \(0.50613\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1288.2.a.d

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