Properties

Label 1088i
Number of curves 4
Conductor 1088
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1088.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1088i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1088.d4 1088i1 [0, 1, 0, -193, -705] [2] 384 \(\Gamma_0(N)\)-optimal
1088.d3 1088i2 [0, 1, 0, -2753, -56513] [2] 768  
1088.d2 1088i3 [0, 1, 0, -6593, 203839] [2] 1152  
1088.d1 1088i4 [0, 1, 0, -7233, 161215] [2] 2304  

Rank

sage: E.rank()
 

The elliptic curves in class 1088i have rank \(0\).

Modular form 1088.2.a.d

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + 4q^{7} + q^{9} + 6q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.