Properties

Label 882.i
Number of curves 6
Conductor 882
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("882.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 882.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
882.i1 882i6 [1, -1, 1, -1204160, -508296477] [2] 6912  
882.i2 882i5 [1, -1, 1, -75200, -7941405] [2] 3456  
882.i3 882i4 [1, -1, 1, -15665, -614631] [2] 2304  
882.i4 882i2 [1, -1, 1, -4640, 122721] [2] 768  
882.i5 882i1 [1, -1, 1, -230, 2769] [2] 384 \(\Gamma_0(N)\)-optimal
882.i6 882i3 [1, -1, 1, 1975, -57207] [2] 1152  

Rank

sage: E.rank()
 

The elliptic curves in class 882.i have rank \(0\).

Modular form 882.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} + 4q^{13} + q^{16} + 6q^{17} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.