Properties

Label 1088.l
Number of curves 4
Conductor 1088
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1088.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1088.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1088.l1 1088c4 [0, -1, 0, -7233, -161215] [2] 2304  
1088.l2 1088c3 [0, -1, 0, -6593, -203839] [2] 1152  
1088.l3 1088c2 [0, -1, 0, -2753, 56513] [2] 768  
1088.l4 1088c1 [0, -1, 0, -193, 705] [2] 384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1088.l have rank \(1\).

Modular form 1088.2.a.l

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 LMFDB 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 LMFDB labels.