Properties

Label 1176c
Number of curves $4$
Conductor $1176$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 1176c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1176.a3 1176c1 \([0, -1, 0, -359, 2724]\) \(2725888/21\) \(39530064\) \([4]\) \(384\) \(0.28677\) \(\Gamma_0(N)\)-optimal
1176.a2 1176c2 \([0, -1, 0, -604, -1196]\) \(810448/441\) \(13282101504\) \([2, 2]\) \(768\) \(0.63334\)  
1176.a1 1176c3 \([0, -1, 0, -7464, -245412]\) \(381775972/567\) \(68307950592\) \([2]\) \(1536\) \(0.97991\)  
1176.a4 1176c4 \([0, -1, 0, 2336, -11780]\) \(11696828/7203\) \(-867763964928\) \([2]\) \(1536\) \(0.97991\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 1176c do not have complex multiplication.

Modular form 1176.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} + 2 q^{13} + 2 q^{15} - 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.