Properties

Label 1176.i
Number of curves $6$
Conductor $1176$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("1176.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1176.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1176.i1 1176i5 [0, 1, 0, -18832, 988448] [2] 1536  
1176.i2 1176i3 [0, 1, 0, -3152, -69168] [2] 768  
1176.i3 1176i4 [0, 1, 0, -1192, 14720] [2, 2] 768  
1176.i4 1176i2 [0, 1, 0, -212, -960] [2, 2] 384  
1176.i5 1176i1 [0, 1, 0, 33, -78] [2] 192 \(\Gamma_0(N)\)-optimal
1176.i6 1176i6 [0, 1, 0, 768, 60192] [2] 1536  

Rank

sage: E.rank()
 

The elliptic curves in class 1176.i have rank \(0\).

Modular form 1176.2.a.i

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} + 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.